The concepts of risk aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. The statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and relationships with robust optimization, risk aversion, chance-constrained optimization, and function regularization. Various approaches to model the distributional ambiguity and their calibrations are discussed. The paper also describes the main solution techniques used to the solve the resulting optimization problems.
Révisé le :
Accepté le :
Publié le :
Mots clés : Distributionally robust optimization, Robust optimization, Stochastic optimization, Risk-averse optimization, Chance-constrained optimization, Statistical learning
@article{OJMO_2022__3__A4_0,
author = {Rahimian, Hamed and Mehrotra, Sanjay},
title = {Frameworks and {Results} in {Distributionally} {Robust} {Optimization}},
journal = {Open Journal of Mathematical Optimization},
eid = {4},
pages = {1--85},
publisher = {Universit\'e de Montpellier},
volume = {3},
year = {2022},
doi = {10.5802/ojmo.15},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/ojmo.15/}
}
TY - JOUR AU - Rahimian, Hamed AU - Mehrotra, Sanjay TI - Frameworks and Results in Distributionally Robust Optimization JO - Open Journal of Mathematical Optimization PY - 2022 SP - 1 EP - 85 VL - 3 PB - Université de Montpellier UR - http://archive.numdam.org/articles/10.5802/ojmo.15/ DO - 10.5802/ojmo.15 LA - en ID - OJMO_2022__3__A4_0 ER -
%0 Journal Article %A Rahimian, Hamed %A Mehrotra, Sanjay %T Frameworks and Results in Distributionally Robust Optimization %J Open Journal of Mathematical Optimization %D 2022 %P 1-85 %V 3 %I Université de Montpellier %U http://archive.numdam.org/articles/10.5802/ojmo.15/ %R 10.5802/ojmo.15 %G en %F OJMO_2022__3__A4_0
Rahimian, Hamed; Mehrotra, Sanjay. Frameworks and Results in Distributionally Robust Optimization. Open Journal of Mathematical Optimization, Tome 3 (2022), article no. 4, 85 p. doi : 10.5802/ojmo.15. http://archive.numdam.org/articles/10.5802/ojmo.15/
[1] Distributionally robust Markovian traffic equilibrium, Transport. Sci., Volume 53 (2019) no. 6, pp. 1546-1562 | DOI
[2] Spectral measures of risk: A coherent representation of subjective risk aversion, J. Bank. Financ., Volume 26 (2002) no. 7, pp. 1505-1518 | DOI
[3] Decision making under uncertainty when preference information is incomplete, Manage. Sci., Volume 61 (2015) no. 1, pp. 111-128 | DOI
[4] Coherent Measures of Risk, Math. Financ., Volume 9 (1999) no. 3, pp. 203-228 | DOI | MR | Zbl
[5] An information-theoretic approach to constructing coherent risk measures, 2011 IEEE International Symposium on Information Theory Proceedings, IEEE (2011), pp. 2125-2127 | DOI
[6] Entropic value-at-risk: A new coherent risk measure, J. Optim. Theory Appl., Volume 155 (2012) no. 3, pp. 1105-1123 | DOI | MR | Zbl
[7] Scenario reduction for stochastic programs with Conditional Value-at-Risk, Math. Program., Volume 170 (2018) no. 1, pp. 327-356 | DOI | MR | Zbl
[8] Robust Optimization of Sums of Piecewise Linear Functions with Application to Inventory Problems, Oper. Res., Volume 64 (2016) no. 2, pp. 474-494 | DOI | MR | Zbl
[9] Models and formulations for multivariate dominance-constrained stochastic programs, IIE Trans., Volume 47 (2015) no. 1, pp. 1-14 | DOI
[10] On distributionally robust multiperiod stochastic optimization, Comput. Manag. Sci., Volume 11 (2014) no. 3, pp. 197-220 | DOI | MR | Zbl
[11] Constructing uncertainty sets for robust linear optimization, Oper. Res., Volume 57 (2009) no. 6, pp. 1483-1495 | DOI | MR | Zbl
[12] Theory and applications of robust optimization, SIAM Rev., Volume 53 (2011) no. 3, pp. 464-501 | DOI | MR | Zbl
[13] Finite adaptability in multistage linear optimization, IEEE Trans. Autom. Control, Volume 55 (2010) no. 12, pp. 2751-2766 | DOI | MR | Zbl
[14] A dynamic mechanism and surplus extraction under ambiguity, J. Econ. Theory, Volume 144 (2009) no. 5, pp. 2084-2114 | DOI | MR | Zbl
[15] Relative robust and adaptive optimization, INFORMS J. Comput., Volume 32 (2020) no. 2, pp. 408-427 | MR | Zbl
[16] Models for minimax stochastic linear optimization problems with risk aversion, Math. Oper. Res., Volume 35 (2010) no. 3, pp. 580-602 | DOI | MR | Zbl
[17] Algorithms for the solution of stochastic dynamic minimax problems, Comput. Optim. Appl., Volume 4 (1995) no. 4, pp. 317-345 | DOI | MR | Zbl
[18] Nonlinear Programming, Athena Scientific, 2016
[19] Dynamic programming and optimal control, Athena Scientific, 2017
[20] Theory of games and statistical decisions, Dover Publications, 1979
[21] Data-driven robust optimization, Math. Program., Volume 167 (2018) no. 2, pp. 235-292 | DOI | MR | Zbl
[22] Robust sample average approximation, Math. Program., Volume 171 (2018) no. 1, pp. 217-282 | DOI | MR | Zbl
[23] Dynamic procurement of new products with covariate information: The residual tree method, Manuf. Serv. Oper. Management, Volume 21 (2019) no. 4, pp. 798-815
[24] Decomposition algorithms for two-stage distributionally robust mixed binary programs, SIAM J. Optim., Volume 28 (2018) no. 3, pp. 2360-2383 | DOI | MR | Zbl
[25] Distributionally robust groupwise regularization estimator, Asian Conference on Machine Learning, Proceedings of Machine Learning Research (2017), pp. 97-112
[26] From predictive to prescriptive analytics, Manage. Sci., Volume 66 (2020) no. 3, pp. 1025-1044 | DOI
[27] Semi-supervised Learning Based on Distributionally Robust Optimization, Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods (Makrides, Andreas; Karagrigoriou, Alex; Skiadas, Christos H, eds.), Volume 5, John Wiley & Sons, 2020, pp. 1-33
[28] Sample out-of-sample inference based on Wasserstein distance, Oper. Res., Volume 69 (2021) no. 3, pp. 985-1013 | DOI | MR | Zbl
[29] Robust Wasserstein profile inference and applications to machine learning, J. Appl. Probab., Volume 56 (2019) no. 3, pp. 830-857 | DOI | MR | Zbl
[30] Data-driven optimal transport cost selection for distributionally robust optimization, Proceedings of the 2019 Winter Simulation Conference (WSC ’19) (2019), pp. 3740-3751 | DOI
[31] Doubly Robust Data-driven Distributionally Robust Optimization, Applied Modeling Techniques and Data Analysis 1 (Dimotikalis, Yannis; Karagrigoriou, Alex; Parpoula, Christina; Skiadas, Christos H, eds.), John Wiley & Sons, pp. 75-90 | DOI
[32] Introduction to Stochastic Programming, Springer, 2011 | DOI
[33] Data-Driven Stochastic Programming Using Phi-Divergences, The Operations Research Revolution, INFORMS TutORials in Operations Research, 2015, pp. 1-19 | Zbl
[34] Rademacher and Gaussian complexities: Risk bounds and structural results, J. Mach. Learn. Res., Volume 3 (2002) no. Nov, pp. 463-482 | MR
[35] Assessing solution quality in stochastic programs, Math. Program., Volume 108 (2006) no. 2-3, pp. 495-514 | DOI | MR | Zbl
[36] Assessing solution quality in stochastic programs via sampling, Decision Technologies and Applications, INFORMS TutORials in Operations Research, 2009, pp. 102-122
[37] Quantifying distributional model risk via optimal transport, Math. Oper. Res., Volume 44 (2019) no. 2, pp. 565-600 | DOI | MR | Zbl
[38] On Solving Two-Stage Distributionally Robust Disjunctive Programs with a General Ambiguity Set, Eur. J. Oper. Res., Volume 279 (2019) no. 2, pp. 296-307 | DOI | MR | Zbl
[39] Statistical Analysis of Wasserstein Distributionally Robust Estimators, Emerging Optimization Methods and Modeling Techniques with Applications, INFORMS TutORials in Operations Research, 2021, pp. 227-254
[40] Dynamic optimization with side information, Eur. J. Oper. Res. (2022) (https://doi.org/10.1016/j.ejor.2022.03.030) | DOI
[41] Optimal Transport-Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes, Math. Oper. Res. (2021) | Zbl
[42] Probabilistic combinatorial optimization: Moments, semidefinite programming, and asymptotic bounds, SIAM J. Optim., Volume 15 (2004) no. 1, pp. 185-209 | DOI | MR | Zbl
[43] Persistence in discrete optimization under data uncertainty, Math. Program., Volume 108 (2006) no. 2-3, pp. 251-274 | DOI | MR | Zbl
[44] Optimal inequalities in probability theory: A convex optimization approach, SIAM J. Optim., Volume 15 (2005) no. 3, pp. 780-804 | DOI | MR | Zbl
[45] Robust linear optimization under general norms, Oper. Res. Lett., Volume 32 (2004) no. 6, pp. 510-516 | DOI | MR | Zbl
[46] The Big Data Newsvendor: Practical Insights from Machine Learning, Oper. Res., Volume 67 (2019) no. 1, pp. 90-108 | MR | Zbl
[47] The price of robustness, Oper. Res., Volume 52 (2004) no. 1, pp. 35-53 | DOI | MR | Zbl
[48] Perturbation analysis of optimization problems, Springer, 2013
[49] Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, 2006 | DOI
[50] A data-driven approach to multistage stochastic linear optimization, Manage. Sci. (2022) (https://doi.org/10.1287/mnsc.2022.4352) | DOI | Zbl
[51] Two-stage sample robust optimization, Oper. Res., Volume 70 (2022) no. 1, pp. 624-640 | DOI | MR | Zbl
[52] A practicable framework for distributionally robust linear optimization, 2014 (Optimization Online www.optimization-online.org/DB_FILE/2013/07/3954.html)
[53] Adaptive distributionally robust optimization, Manage. Sci., Volume 65 (2019) no. 2, pp. 604-618 | DOI
[54] A soft robust model for optimization under ambiguity, Oper. Res., Volume 58 (2010) no. 4, Part 2, pp. 1220-1234 | DOI | MR | Zbl
[55] Globalized robust optimization for nonlinear uncertain inequalities, INFORMS J. Comput., Volume 29 (2017) no. 2, pp. 350-366 | DOI | MR | Zbl
[56] Extending scope of robust optimization: Comprehensive robust counterparts of uncertain problems, Math. Program., Volume 107 (2006) no. 1-2, pp. 63-89 | DOI | MR | Zbl
[57] Robust solutions of optimization problems affected by uncertain probabilities, Manage. Sci., Volume 59 (2013) no. 2, pp. 341-357 | DOI
[58] Deriving robust counterparts of nonlinear uncertain inequalities, Math. Program., Volume 149 (2015) no. 1-2, pp. 265-299 | DOI | MR | Zbl
[59] Robust Optimization, Princeton University Press, 2009 | DOI
[60] Adjustable robust solutions of uncertain linear programs, Math. Program., Volume 99 (2004) no. 2, pp. 351-376 | DOI | MR | Zbl
[61] More bounds on the expectation of a convex function of a random variable, J. Appl. Probab., Volume 9 (1972) no. 4, pp. 803-812 | MR | Zbl
[62] Robust solutions of linear programming problems contaminated with uncertain data, Math. Program., Volume 88 (2000) no. 3, pp. 411-424 | DOI | MR | Zbl
[63] On safe tractable approximations of chance-constrained linear matrix inequalities, Math. Oper. Res., Volume 34 (2009) no. 1, pp. 1-25 | DOI | MR | Zbl
[64] Lectures on modern convex optimization: Analysis, Algorithms, Engineering Applications, MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics, 2019
[65] Robust convex optimization, Math. Oper. Res., Volume 23 (1998) no. 4, pp. 769-805 | DOI | MR
[66] An Old-New Concept of Convex Risk Measures: The Optimized Certainty Equivalent, Math. Financ., Volume 17 (2007) no. 3, pp. 449-476 | DOI | MR | Zbl
[67] Expected utility, penalty functions, and duality in stochastic nonlinear programming, Manage. Sci., Volume 32 (1986) no. 11, pp. 1445-1466 | DOI | MR | Zbl
[68] Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities (6), Volume 14 (2005) no. 3, pp. 331-352 | Numdam | Zbl
[69] Bootstrap robust prescriptive analytics, Math. Program. (2021) (https://doi.org/10.1007/s10107-021-01679-2) | DOI
[70] Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions (2021) (https://arxiv.org/abs/2109.06911)
[71] Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs, J. Glob. Optim., Volume 81 (2021) no. 2, pp. 391-433 | DOI | MR | Zbl
[72] Ambiguous risk measures and optimal robust portfolios, SIAM J. Optim., Volume 18 (2007) no. 3, pp. 853-877 | DOI | MR | Zbl
[73] Wasserstein distance and the distributionally robust TSP, Oper. Res., Volume 66 (2018) no. 6, pp. 1603-1624 | DOI | MR | Zbl
[74] Decision making in an uncertain environment: the scenario-based optimization approach, Multiple Participant Decision Making, Advanced Knowledge International, 2004, pp. 99-111
[75] Uncertain convex programs: randomized solutions and confidence levels, Math. Program., Volume 102 (2005) no. 1, pp. 25-46 | DOI | MR | Zbl
[76] Chance-constrained programming, Manage. Sci., Volume 6 (1959) no. 1, pp. 73-79 | DOI | MR | Zbl
[77] Deterministic equivalents for optimizing and satisficing under chance constraints, Oper. Res., Volume 11 (1963) no. 1, pp. 18-39 | DOI | MR | Zbl
[78] Duality, Haar programs, and finite sequence spaces, Proc. Natl. Acad. Sci. USA, Volume 48 (1962) no. 5, pp. 783-786 | DOI | MR | Zbl
[79] Duality in semi-infinite programs and some works of Haar and Carathéodory, Manage. Sci., Volume 9 (1963) no. 2, pp. 209-228 | DOI | Zbl
[80] On the theory of semi-infinite programming and a generalization of the Kuhn-Tucker saddle point theorem for arbitrary convex functions, Nav. Res. Logist. Q., Volume 16 (1969) no. 1, pp. 41-52 | DOI | MR | Zbl
[81] Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil, Manage. Sci., Volume 4 (1958) no. 3, pp. 235-263 | DOI
[82] On distributionally robust chance-constrained linear programs, J. Optim. Theory Appl., Volume 130 (2006) no. 1, pp. 1-22 | DOI | MR | Zbl
[83] The exact feasibility of randomized solutions of uncertain convex programs, SIAM J. Optim., Volume 19 (2008) no. 3, pp. 1211-1230 | DOI | MR | Zbl
[84] Data-Driven Chance Constrained Programs over Wasserstein Balls (2018) (https://arxiv.org/abs/1809.00210)
[85] Distributionally Robust Optimization with Principal Component Analysis, SIAM J. Optim., Volume 28 (2018) no. 2, pp. 1817-1841 | DOI | MR | Zbl
[86] Distributionally robust linear and discrete optimization with marginals, Oper. Res. (2022) (https://doi.org/10.1287/opre.2021.2243) | MR
[87] A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., Volume 40 (2011) no. 1, pp. 120-145 | DOI | MR | Zbl
[88] A Robust Learning Approach for Regression Models Based on Distributionally Robust Optimization, J. Mach. Learn. Res., Volume 19 (2018) no. 13, pp. 1-48 | MR | Zbl
[89] et al. Consistency and robustness of kernel-based regression in convex risk minimization, Bernoulli, Volume 13 (2007) no. 3, pp. 799-819 | MR | Zbl
[90] On robustness properties of convex risk minimization methods for pattern recognition, J. Mach. Learn. Res., Volume 5 (2004) no. Aug, pp. 1007-1034 | MR | Zbl
[91] Goal-driven optimization, Oper. Res., Volume 57 (2009) no. 2, pp. 342-357 | DOI | MR | Zbl
[92] A robust optimization perspective on stochastic programming, Oper. Res., Volume 55 (2007) no. 6, pp. 1058-1071 | DOI | MR | Zbl
[93] From CVaR to uncertainty set: Implications in joint chance-constrained optimization, Oper. Res., Volume 58 (2010) no. 2, pp. 470-485 | DOI | MR | Zbl
[94] A linear decision-based approximation approach to stochastic programming, Oper. Res., Volume 56 (2008) no. 2, pp. 344-357 | DOI | MR | Zbl
[95] Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems, Math. Program., Volume 177 (2019) no. 1, pp. 255-289 | DOI | MR | Zbl
[96] Distributionally robust optimization with infinitely constrained ambiguity sets, Oper. Res., Volume 67 (2019) no. 5, pp. 1328-1344 | DOI | MR | Zbl
[97] Robust stochastic optimization made easy with RSOME, Manage. Sci., Volume 66 (2020) no. 8, pp. 3329-3339 | DOI
[98] Decomposition and discrete approximation methods for solving two-stage distributionally robust optimization problems, Comput. Optim. Appl., Volume 78 (2021) no. 1, pp. 205-238 | DOI | MR | Zbl
[99] RSOME in Python: An Open-Source Package for Robust Stochastic Optimization Made Easy, 2021 (Optimization Online http://www.optimization-online.org/DB_HTML/2021/06/8443.html)
[100] Regret in the newsvendor model with demand and yield randomness, Prod. Oper. Manage., Volume 30 (2021) no. 11, pp. 4176-4197 | DOI
[101] Uncertain linear programs: Extended affinely adjustable robust counterparts, Oper. Res., Volume 57 (2009) no. 6, pp. 1469-1482 | DOI | MR | Zbl
[102] Worst-case expected shortfall with univariate and bivariate marginals, INFORMS J. Comput., Volume 33 (2021) no. 1, pp. 370-389 | DOI | MR | Zbl
[103] Distributionally robust optimization in context of data-driven problems, Ph.D. dissertation, Stanford University (2009)
[104] Optimization Models with Probabilistic Constraints, Probabilistic and Randomized Methods for Design under Uncertainty (Calafiore, Giuseppe C.; Dabbene, Fabrizio, eds.), Springer, 2006, pp. 49-97 | DOI | Zbl
[105] Nonparametric density estimation: The L1 View, John Wiley & Sons, 1985
[106] Scenario reduction in stochastic programming, Math. Program., Volume 95 (2003) no. 3, pp. 493-511 | DOI | Zbl
[107] Statistics of robust optimization: A generalized empirical likelihood approach, Math. Oper. Res., Volume 46 (2021) no. 3, pp. 946-969 | DOI | MR | Zbl
[108] Shortfall Risk Models When Information on Loss Function Is Incomplete, Oper. Res. (2022)
[109] JuMP: A Modeling Language for Mathematical Optimization, SIAM Rev., Volume 59 (2017) no. 2, pp. 295-320 | DOI | MR | Zbl
[110] Distributionally Robust Losses Against Mixture Covariate Shifts (2019) (https://arxiv.org/abs/2007.13982)
[111] Globalized distributionally robust optimization problems under the moment-based framework (2020) (https://arxiv.org/abs/2008.08256)
[112] Unimodality, convexity, and applications, Academic Press Inc., 1988
[113] Path-space information bounds for uncertainty quantification and sensitivity analysis of stochastic dynamics, SIAM/ASA J. Uncertain. Quantif., Volume 4 (2016) no. 1, pp. 80-111 | DOI | MR | Zbl
[114] "Dice“sion-Making Under Uncertainty: When Can a Random Decision Reduce Risk?, Manage. Sci., Volume 65 (2019) no. 7, pp. 3282-3301 | DOI
[115] Minimizing risk exposure when the choice of a risk measure is ambiguous, Manage. Sci., Volume 64 (2018) no. 1, pp. 327-344 | DOI
[116] Robustness to dependency in portfolio optimization using overlapping marginals, Oper. Res., Volume 63 (2015) no. 6, pp. 1468-1488 | DOI | MR | Zbl
[117] Distributionally robust stochastic dual dynamic programming, SIAM J. Optim., Volume 30 (2020) no. 4, pp. 2841-2865 | DOI | MR | Zbl
[118] Distributional robustness and regularization in reinforcement learning (2020) (https://arxiv.org/abs/2003.02894)
[119] Portfolio selection with robust estimation, Oper. Res., Volume 57 (2009) no. 3, pp. 560-577 | DOI | MR | Zbl
[120] Optimization with stochastic dominance constraints, SIAM J. Optim., Volume 14 (2003) no. 2, pp. 548-566 | DOI | MR | Zbl
[121] Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints, Math. Program., Volume 99 (2004) no. 2, pp. 329-350 | DOI | MR | Zbl
[122] Optimization with multivariate stochastic dominance constraints, Math. Program., Volume 117 (2009) no. 1-2, pp. 111-127 | DOI | MR | Zbl
[123] Robust stochastic dominance and its application to risk-averse optimization, Math. Program., Volume 123 (2010) no. 1, pp. 85-100 | DOI | MR | Zbl
[124] Learning Enabled Optimization: Towards a Fusion of Statistical Learning and Stochastic Optimization, 2018 (Optimization Online http://www.optimization-online.org/DB_HTML/2017/03/5904.html)
[125] The value of randomized solutions in mixed-integer distributionally robust optimization problems, INFORMS J. Comput., Volume 34 (2022) no. 1, pp. 333-353 | DOI | MR | Zbl
[126] The speed of mean Glivenko-Cantelli convergence, Ann. Math. Stat., Volume 40 (1969) no. 1, pp. 40-50 | DOI | MR | Zbl
[127] Advances in robust and adaptive optimization: algorithms, software, and insights, Ph. D. Thesis, Massachusetts Institute of Technology (2016)
[128] The minimax approach to stochastic programming and an illustrative application, Stochastics, Volume 20 (1987) no. 1, pp. 73-88 | DOI | MR | Zbl
[129] Stability and sensitivity-analysis for stochastic programming, Ann. Oper. Res., Volume 27 (1990) no. 1, pp. 115-142 | DOI | MR | Zbl
[130] Distributionally robust optimization under moment uncertainty with application to data-driven problems, Oper. Res., Volume 58 (2010) no. 3, pp. 595-612 | DOI | MR | Zbl
[131] Large deviations techniques and applications, Stochastic Modelling and Applied Probability, 38, Springer, 1998 | DOI
[132] Robust solutions to least-squares problems with uncertain data, SIAM J. Matrix Anal. Appl., Volume 18 (1997) no. 4, pp. 1035-1064 | DOI | MR | Zbl
[133] Robust solutions to uncertain semidefinite programs, SIAM J. Optim., Volume 9 (1998) no. 1, pp. 33-52 | DOI | MR | Zbl
[134] Worst-case value-at-risk and robust portfolio optimization: A conic programming approach, Oper. Res., Volume 51 (2003) no. 4, pp. 543-556 | MR | Zbl
[135] Ambiguous chance constrained problems and robust optimization, Math. Program., Volume 107 (2006) no. 1-2, pp. 37-61 | DOI | MR | Zbl
[136] Discrete Chebyshev classifiers, 31st International Conference on Machine Learning, Proceedings of Machine Learning Research (2014), pp. 1233-1241
[137] Aggregating risk capital, with an application to operational risk, Geneva Risk Insur. Rev., Volume 31 (2006) no. 2, pp. 71-90 | DOI
[138] Bounds for functions of multivariate risks, J. Multivariate Anal., Volume 97 (2006) no. 2, pp. 526-547 | DOI | MR | Zbl
[139] Distributionally robust stochastic programs with side information based on trimmings, Math. Program. (2021) (https://doi.org/10.1007/s10107-021-01724-0) | DOI
[140] On the rate of convergence in Wasserstein distance of the empirical measure, Probab. Theory Relat. Fields, Volume 162 (2015) no. 3-4, pp. 707-738 | DOI | MR | Zbl
[141] The elements of statistical learning, Springer Series in Statistics, Springer, 2016
[142] Light robustness, Robust and online large-scale optimization: models and techniques for transportation systems (Ahuja, Ravindra K; Möhring, Rolf H; Zaroliagis, Christos D, eds.), Springer, 2009, pp. 61-84 | DOI | Zbl
[143] Distributionally Robust Graphical Models, Advances in Neural Information Processing Systems 31 (Bengio, S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R., eds.), Curran Associates, Inc. (2018), pp. 8354-8365
[144] A Minimax Approach to Supervised Learning, Advances in Neural Information Processing Systems 29 (Lee, D. D.; Sugiyama, M.; Luxburg, U. V.; Guyon, I.; Garnett, R., eds.), Curran Associates, Inc., 2016, pp. 4240-4248
[145] Handbook of simulation optimization, International Series in Operations Research & Management Science (Price, Camille C., ed.), Springer, 2016 | Zbl
[146] Wasserstein distributional robustness and regularization in statistical learning (2017) (https://arxiv.org/abs/1712.06050)
[147] Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory, Ann. Stat., Volume 32 (2004) no. 4, pp. 1367-1433 | MR | Zbl
[148] Robust portfolio selection problems, Math. Oper. Res., Volume 28 (2003) no. 1, pp. 1-38 | DOI | MR | Zbl
[149] Distributionally robust stochastic optimization with Wasserstein distance (2016) (https://arxiv.org/abs/1604.02199v2)
[150] Distributionally robust stochastic optimization with dependence structure (2017) (https://arxiv.org/abs/1701.04200)
[151] Robust empirical optimization is almost the same as mean–variance optimization, Oper. Res. Lett., Volume 46 (2018) no. 4, pp. 448-452 | DOI | MR | Zbl
[152] Calibration of distributionally robust empirical optimization models, Oper. Res., Volume 69 (2021) no. 5, pp. 1630-1650 | DOI | MR | Zbl
[153] The decision rule approach to optimization under uncertainty: methodology and applications, Comput. Manag. Sci., Volume 16 (2019) no. 4, pp. 545-576 | DOI | MR | Zbl
[154] Distributionally robust L1-estimation in multiple linear regression, Optim. Lett., Volume 13 (2019) no. 4, pp. 935-947 | DOI | Zbl
[155] The distribution free newsboy problem: review and extensions, J. Oper. Res. Soc., Volume 44 (1993) no. 8, pp. 825-834 | DOI | Zbl
[156] Recent advances in robust optimization: An overview, Eur. J. Oper. Res., Volume 235 (2014) no. 3, pp. 471-483 | DOI | MR | Zbl
[157] Incorporating statistical model error into the calculation of acceptability prices of contingent claims, Math. Program., Volume 174 (2019) no. 1-2, pp. 499-524 | DOI | MR | Zbl
[158] On choosing and bounding probability metrics, Int. Stat. Rev., Volume 70 (2002) no. 3, pp. 419-435 | DOI | Zbl
[159] Distributionally robust optimization and its tractable approximations, Oper. Res., Volume 58 (2010) no. 4, Part 1, pp. 902-917 | MR | Zbl
[160] Robust Optimization Made Easy with ROME, Oper. Res., Volume 59 (2011) no. 4, pp. 973-985 | MR | Zbl
[161] Maxmin expected utility with non-unique prior, J. Math. Econ., Volume 18 (1989) no. 2, pp. 141-153 | DOI | Zbl
[162] The minimum information principle for discriminative learning, Proceedings of the 20th conference on Uncertainty in artificial intelligence, AUAI Press (2004), pp. 193-200
[163] Robust risk measurement and model risk, Quant. Finance, Volume 14 (2014) no. 1, pp. 29-58 | DOI | MR | Zbl
[164] Robust Hypothesis Testing Using Wasserstein Uncertainty Sets, Advances in Neural Information Processing Systems (Bengio, S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R., eds.), Volume 31, Curran Associates, Inc. (2018)
[165] Convergence analysis for mathematical programs with distributionally robust chance constraint, SIAM J. Optim., Volume 27 (2017) no. 2, pp. 784-816 | MR | Zbl
[166] Bounding Wrong-Way Risk in CVA Calculation, Math. Financ., Volume 28 (2018) no. 1, pp. 268-305 | DOI | MR | Zbl
[167] A practical guide to robust optimization, Omega, Volume 53 (2015), pp. 124-137 | DOI
[168] Minimax robust hypothesis testing, IEEE Trans. Inf. Theory, Volume 63 (2017) no. 9, pp. 5572-5587 | MR | Zbl
[169] Asymptotically Minimax Robust Hypothesis Testing (2017) (https://arxiv.org/abs/1711.07680)
[170] Üher linear Ungleichungen, Acta Sci. Math., Volume 2 (1924)
[171] Monte Carlo sampling-based methods for stochastic optimization, Surv. Oper. Res. Manage. Sci., Volume 19 (2014) no. 1, pp. 56-85 | MR
[172] Technical Note-A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula, Oper. Res., Volume 62 (2014) no. 3, pp. 535-542 | MR | Zbl
[173] Kullback-Leibler divergence constrained distributionally robust optimization, 2012 (Optimization Online http://www.optimization-online.org/DB_HTML/2012/11/3677.html)
[174] Risk-adjusted budget allocation models with application in homeland security, IIE Trans., Volume 43 (2011) no. 12, pp. 819-839
[175] Sample average approximation of stochastic dominance constrained programs, Math. Program., Volume 133 (2012) no. 1-2, pp. 171-201 | MR | Zbl
[176] Stochastically weighted stochastic dominance concepts with an application in capital budgeting, Eur. J. Oper. Res., Volume 232 (2014) no. 3, pp. 572-583 | MR | Zbl
[177] Ambiguous probabilistic programs, 2013 (Optimization Online http://www.optimization-online.org/DB_HTML/2013/09/4039.html)
[178] On first and second order conditions for local optima for optimization problems in finite dimensions, Methods Oper. Res., Volume 23 (1977), pp. 82-97 | Zbl
[179] Semi-infinite programming: conditions of optimality and applications, Optimization Techniques, Lecture Notes in Control and Information Science (Stoer, J, ed.), Springer, 1978, pp. 82-97 | Zbl
[180] Robust Data-Driven Dynamic Programming, Advances in Neural Information Processing Systems 26 (Burges, C. J. C.; Bottou, L.; Welling, M.; Ghahramani, Z.; Weinberger, K. Q., eds.), Curran Associates, Inc., 2013, pp. 827-835
[181] Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls, Oper. Res., Volume 66 (2018) no. 3, pp. 849-869 | DOI | MR | Zbl
[182] Semi-infinite programming: theory, methods, and applications, SIAM Rev., Volume 35 (1993) no. 3, pp. 380-429 | DOI | MR | Zbl
[183] K-adaptability in two-stage robust binary programming, Oper. Res., Volume 63 (2015) no. 4, pp. 877-891 | DOI | MR | Zbl
[184] K-adaptability in two-stage distributionally robust binary programming, Oper. Res. Lett., Volume 44 (2016) no. 1, pp. 6-11 | DOI | MR | Zbl
[185] Distributionally robust multi-item newsvendor problems with multimodal demand distributions, Math. Program., Volume 152 (2015) no. 1-2, pp. 1-32 | DOI | MR | Zbl
[186] A data-driven functionally robust approach for simultaneous pricing and order quantity decisions with unknown demand function, Oper. Res., Volume 67 (2019) no. 6, pp. 1564-1585 | MR | Zbl
[187] et al. Pyomo-optimization modeling in Python, Springer, 2017 | DOI
[188] A cutting-surface method for uncertain linear programs with polyhedral stochastic dominance constraints, SIAM J. Optim., Volume 20 (2009) no. 3, pp. 1250-1273 | DOI | MR | Zbl
[189] Robust and stochastically weighted multiobjective optimization models and reformulations, Oper. Res., Volume 60 (2012) no. 4, pp. 936-953 | MR | Zbl
[190] Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization, IIE Trans., Volume 47 (2015) no. 4, pp. 358-372
[191] Strong formulations for distributionally robust chance-constrained programs with left-hand side uncertainty under Wasserstein ambiguity (2020) (https://arxiv.org/abs/2007.06750)
[192] Distributionally robust chance-constrained programs with right-hand side uncertainty under Wasserstein ambiguity, Math. Program. (2021) (https://doi.org/10.1007/s10107-020-01605-y) | DOI
[193] Does Distributionally Robust Supervised Learning Give Robust Classifiers?, 35th International Conference on Machine Learning, Proceedings of Machine Learning Research (2018), pp. 2034-2042
[194] Nonparametric Density Estimation for Stochastic Optimization with an Observable State Variable, Advances in Neural Information Processing Systems 23 (Lafferty, J. D.; Williams, C. K. I.; Shawe-Taylor, J.; Zemel, R. S.; Culotta, A., eds.), Curran Associates, Inc., 2010, pp. 820-828
[195] Scenario reduction algorithms in stochastic programming, Comput. Optim. Appl., Volume 24 (2003) no. 2-3, pp. 187-206 | DOI | MR | Zbl
[196] Scenario tree modeling for multistage stochastic programs, Math. Program., Volume 118 (2009) no. 2, pp. 371-406 | DOI | MR | Zbl
[197] Scenario tree reduction for multistage stochastic programs, Comput. Manag. Sci., Volume 6 (2009) no. 2, pp. 117-133 | DOI | MR | Zbl
[198] Robust Statistics, John Wiley & Sons, 2009 | DOI
[199] A distributionally robust perspective on uncertainty quantification and chance constrained programming, Math. Program., Volume 151 (2015) no. 1, pp. 35-62 | DOI | MR | Zbl
[200] Ambiguous joint chance constraints under mean and dispersion information, Oper. Res., Volume 65 (2017) no. 3, pp. 751-767 | DOI | MR | Zbl
[201] Stability of multistage stochastic programs, SIAM J. Optim., Volume 17 (2006) no. 2, pp. 511-525 | DOI | MR | Zbl
[202] Second order optimality conditions for generalized semi-infinite programming problems, Optimization, Volume 34 (1995) no. 3, pp. 195-211 | DOI | MR
[203] An interior-point method for a class of saddle-point problems, J. Optim. Theory Appl., Volume 116 (2003) no. 3, pp. 559-590 | DOI | MR | Zbl
[204] A robust version of the probability ratio test, Ann. Math. Stat. (1965), pp. 1753-1758 | DOI | MR | Zbl
[205] The use of Choquet capacities in statistics, B. Int. Statist. Inst., Volume 45 (1973) no. 4, pp. 181-191 | MR
[206] The generalized Bayes minimax principle: a criterion for decision making uncer uncertainty, Cowles Comm. Discuss. Paper: Stat. (1951)
[207] A Study of Distributionally Robust Multistage Stochastic Optimization (2017) (https://arxiv.org/abs/1708.07930)
[208] Pyros: A Pyomo Robust Optimization Solver for Robust Process Design, 2020 Virtual AIChE Annual Meeting, AIChE (2020)
[209] On sharpness of Tchebycheff-type inequalities, Ann. Inst. Stat. Math., Volume 14 (1962) no. 1, pp. 185-197 | DOI | MR | Zbl
[210] Data-driven chance constrained stochastic program, Math. Program., Volume 158 (2016) no. 1-2, pp. 291-327 | DOI | MR | Zbl
[211] Risk-averse two-stage stochastic program with distributional ambiguity, Oper. Res., Volume 66 (2018) no. 5, pp. 1390-1405 | DOI | MR | Zbl
[212] Risk-averse stochastic unit commitment with incomplete information, IIE Trans., Volume 48 (2016) no. 9, pp. 838-854 | DOI
[213] Data-driven distributionally robust chance-constrained optimization with Wasserstein metric, J. Glob. Optim., Volume 79 (2021) no. 4, pp. 779-811 | MR | Zbl
[214] Data-driven optimization of reward-risk ratio measures, INFORMS J. Comput., Volume 33 (2021) no. 3, pp. 1120-1137 | MR | Zbl
[215] Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations, Oper. Res., Volume 65 (2017) no. 6, pp. 1638-1656 | DOI | MR | Zbl
[216] An introduction to statistical learning, Springer, 2013 | DOI
[217] Data-driven sample average approximation with covariate information, 2020 (Optimization Online http:/www. optimization-online.org/DB_HTML/2020/07/7932.html)
[218] Residuals-based distributionally robust optimization with covariate information, 2020 (https://arxiv.org/abs/2012.01088)
[219] Worst-case robust Omega ratio, Eur. J. Oper. Res., Volume 234 (2014) no. 2, pp. 499-507 | DOI | MR | Zbl
[220] Wasserstein distributionally robust optimization: Theory and applications in machine learning, Operations Research & Management Science in the Age of Analytics, INFORMS TutORials in Operations Research, 2019, pp. 130-166 | DOI
[221] A two-stage stochastic integer programming approach to integrated staffing and scheduling with application to nurse management, Oper. Res., Volume 63 (2015) no. 6, pp. 1431-1451 | MR | Zbl
[222] Risk, uncertainty and profit, Houghton Mifflin, 1921
[223] Robust Stochastic Lot-Sizing by Means of Histograms, Prod. Oper. Manage., Volume 22 (2013) no. 3, pp. 691-710 | DOI
[224] On law invariant coherent risk measures, Advances in Mathematical Economics (Kusuoka, Shigeo; Maruyama, Toru, eds.), Springer, 2001, pp. 83-95 | DOI | Zbl
[225] Primal and dual linear decision rules in stochastic and robust optimization, Math. Program., Volume 130 (2011) no. 1, pp. 177-209 | DOI | MR | Zbl
[226] A sample approximation approach for optimization with probabilistic constraints, SIAM J. Optim., Volume 19 (2008) no. 2, pp. 674-699 | DOI | MR | Zbl
[227] Advanced tutorial: Input uncertainty and robust analysis in stochastic simulation, Proceedings of the 2016 Winter Simulation Conference (WSC ’16), IEEE (2016), pp. 178-192
[228] Robust sensitivity analysis for stochastic systems, Math. Oper. Res., Volume 41 (2016) no. 4, pp. 1248-1275 | MR | Zbl
[229] Sensitivity to serial dependency of input processes: A robust approach, Manage. Sci., Volume 64 (2018) no. 3, pp. 1311-1327
[230] Recovering best statistical guarantees via the empirical divergence-based distributionally robust optimization, Oper. Res., Volume 67 (2019) no. 4, pp. 1090-1105 | MR | Zbl
[231] Moments in mathematics (Landau, Henry J., ed.), Proceeding of Symposia in Applied Mathematics, 37, American Mathematical Society, 1987 | DOI
[232] Global optimization with polynomials and the problem of moments, SIAM J. Optim., Volume 11 (2001) no. 3, pp. 796-817 | DOI | MR | Zbl
[233] Two-stage likelihood robust linear program with application to water allocation under uncertainty, Proceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World (WSC ’13), IEEE (2013), pp. 77-88 | DOI
[234] Phi-divergence constrained ambiguous stochastic programs for data-driven optimization, 2016 (Optimization Online http://www.optimization-online.org/DB_HTML/2016/03/5350.html)
[235] Globalized Distributionally Robust Counterpart: Model, Reformulation, and Applications, 2021 (Optimization Online http://www.optimization-online.org/DB_HTML/2021/11/8663.html)
[236] A robust minimax approach to classification, J. Mach. Learn. Res., Volume 3 (2002), pp. 555-582 | MR | Zbl
[237] Robust Hypothesis Testing With a Relative Entropy Tolerance, IEEE Trans. Inf. Theory, Volume 55 (2009) no. 1, pp. 413-421 | DOI | MR | Zbl
[238] Technical Note-Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization, Oper. Res., Volume 66 (2018) no. 6, pp. 1533-1541 | MR | Zbl
[239] Ambiguous risk constraints with moment and unimodality information, Math. Program., Volume 173 (2019) no. 1-2, pp. 151-192 | MR | Zbl
[240] Portfolio selection under model uncertainty: a penalized moment-based optimization approach, J. Glob. Optim., Volume 56 (2013) no. 1, pp. 131-164 | MR | Zbl
[241] A new exact penalty method for semi-infinite programming problems, J. Comput. Appl. Math., Volume 261 (2014), pp. 271-286 | DOI | MR | Zbl
[242] A distributionally-robust approach for finding support vector machines, 2015 (Optimization Online http://www.optimization-online.org/DB_HTML/2015/06/4965.html)
[243] Tail analysis without parametric models: A worst-case perspective, Oper. Res., Volume 65 (2017) no. 6, pp. 1696-1711 | MR | Zbl
[244] Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric with an Application to a Class of Regression Models, Eur. J. Oper. Res., Volume 278 (2019) no. 1, pp. 20-35 | MR | Zbl
[245] Distributionally robust optimization with decision dependent ambiguity sets, Optim. Lett., Volume 14 (2020) no. 8, pp. 2565-2594 | MR | Zbl
[246] Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data, Proceedings of the Eighteenth International Conference on Machine Learning (ICML ’01), Morgan Kaufmann Publishers Inc. (2001), pp. 282-289
[247] Distributionally Robust Reward-Risk Ratio Optimization with Moment Constraints, SIAM J. Optim., Volume 27 (2017) no. 2, pp. 957-985 | MR | Zbl
[248] Distributionally robust discrete optimization with Entropic Value-at-Risk, Oper. Res. Lett., Volume 42 (2014) no. 8, pp. 532-538 | DOI | MR | Zbl
[249] Minimax Statistical Learning with Wasserstein distances, Advances in Neural Information Processing Systems 31 (Bengio, S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R., eds.), Curran Associates, Inc., 2018, pp. 2692-2701
[250] Semi-infinite programming, Eur. J. Oper. Res., Volume 180 (2007) no. 2, pp. 491-518 | DOI | MR | Zbl
[251] A review of robust operations management under model uncertainty, Prod. Oper. Manage., Volume 30 (2021) no. 6, pp. 1927-1943
[252] Model uncertainty, robust optimization, and learning, Models, Methods, and Applications for Innovative Decision Making, INFORMS, 2006, pp. 66-94
[253] The Dao of Robustness: Achieving Robustness in Prescriptive Analytics, 2020 (available at SSRN 3478930)
[254] Robust satisficing, Oper. Res. (2022) (https://doi.org/10.1287/opre.2021.2238)
[255] Distributionally robust polynomial chance-constraints under mixture ambiguity sets, Math. Program., Volume 185 (2021) no. 1, pp. 409-453 | DOI | MR | Zbl
[256] Globalized distributionally robust optimization based on samples (2022) (https://arxiv.org/abs/2205.02994)
[257] Primal–dual hybrid gradient method for distributionally robust optimization problems, Oper. Res. Lett., Volume 45 (2017) no. 6, pp. 625-630 | MR | Zbl
[258] Quantifying uncertainty in sample average approximation, Proceedings of the 2015 Winter Simulation Conference (WSC ’15) (2015), pp. 3846-3857
[259] The empirical likelihood approach to quantifying uncertainty in sample average approximation, Oper. Res. Lett., Volume 45 (2017) no. 4, pp. 301-307 | MR | Zbl
[260] Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances, Eur. J. Oper. Res., Volume 269 (2018) no. 2, pp. 556-576 | DOI | MR | Zbl
[261] Concentration, Probabilistic Methods for Algorithmic Discrete Mathematics (Habib, Michel; McDiarmid, Colin; Ramirez-Alfonsin, Jorge; Reed, Bruce, eds.), Springer, 1998, pp. 195-248 | DOI | Zbl
[262] Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations, Math. Program., Volume 171 (2018) no. 1, pp. 115-166 | DOI | MR | Zbl
[263] Data-driven inverse optimization with imperfect information, Math. Program., Volume 167 (2018) no. 1, pp. 191-234 | DOI | MR | Zbl
[264] Distributionally Robust Second-Order Stochastic Dominance Constrained Optimization with Wasserstein Ball, SIAM J. Optim., Volume 32 (2022) no. 2, pp. 715-738 | DOI | MR | Zbl
[265] A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization, SIAM J. Optim., Volume 24 (2014) no. 4, pp. 1670-1697 | DOI | MR | Zbl
[266] Foundations of machine learning, MIT Press, 2018
[267] Data-driven Distributionally Robust Polynomial Optimization, Advances in Neural Information Processing Systems 26 (Burges, C. J. C.; Bottou, L.; Welling, M.; Ghahramani, Z.; Weinberger, K. Q., eds.), Curran Associates, Inc., 2013, pp. 37-45
[268] Robust optimization of large-scale systems, Oper. Res., Volume 43 (1995) no. 2, pp. 264-281 | DOI | MR | Zbl
[269] Models and algorithms for distributionally robust least squares problems, Math. Program., Volume 146 (2014) no. 1-2, pp. 123-141 | DOI | MR | Zbl
[270] Integral probability metrics and their generating classes of functions, Adv. Appl. Probab. (1997), pp. 429-443 | DOI | Zbl
[271] Stochastic Gradient Methods for Distributionally Robust Optimization with f-divergences, Advances in Neural Information Processing Systems 29 (Lee, D. D.; Sugiyama, M.; Luxburg, U. V.; Guyon, I.; Garnett, R., eds.), Curran Associates, Inc., 2016, pp. 2208-2216
[272] Stochastic Gradient Methods for Distributionally Robust Optimization with f-divergences, Advances in Neural Information Processing Systems (Lee, D.; Sugiyama, M.; Luxburg, U.; Guyon, I.; Garnett, R., eds.), Volume 29, Curran Associates, Inc. (2016)
[273] Variance-based Regularization with Convex Objectives, Advances in Neural Information Processing Systems 30 (Guyon, I.; Luxburg, U. V.; Bengio, S.; Wallach, H.; Fergus, R.; Vishwanathan, S.; Garnett, R., eds.), Curran Associates, Inc., 2017, pp. 2971-2980
[274] Robust stochastic approximation approach to stochastic programming, SIAM J. Optim., Volume 19 (2009) no. 4, pp. 1574-1609 | DOI | MR
[275] Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator, Oper. Res., Volume 70 (2022) no. 1, pp. 490-515 | DOI | MR | Zbl
[276] Search and Knightian uncertainty, J. Econ. Theory, Volume 119 (2004) no. 2, pp. 299-333 | DOI | MR | Zbl
[277] An Axiomatic Approach to -Contamination, J. Econ. Theory, Volume 27 (2006) no. 2, pp. 333-340 | DOI | MR | Zbl
[278] Constructing risk measures from uncertainty sets, Oper. Res., Volume 57 (2009) no. 5, pp. 1129-1141 | DOI | MR | Zbl
[279] Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics, INFORMS J. Comput., Volume 34 (2022) no. 2, pp. 729-751 | DOI | MR | Zbl
[280] Convex approximations of chance constrained programs, SIAM J. Optim., Volume 17 (2006) no. 4, pp. 969-996 | DOI | MR | Zbl
[281] Scenario Approximations of Chance Constraints, Probabilistic and Randomized Methods for Design under Uncertainty (Calafiore, Giuseppe C.; Dabbene, Fabrizio, eds.), Springer, 2006, pp. 3-47 | DOI | Zbl
[282] A Probabilistic Model for Minmax Regret in Combinatorial Optimization, Oper. Res., Volume 62 (2014) no. 1, pp. 160-181 | DOI | MR | Zbl
[283] On reduced semidefinite programs for second order moment bounds with applications, Math. Program., Volume 161 (2017) no. 1-2, pp. 487-518 | DOI | MR | Zbl
[284] Mixed 0-1 linear programs under objective uncertainty: A completely positive representation, Oper. Res., Volume 59 (2011) no. 3, pp. 713-728 | DOI | MR | Zbl
[285] Mixed 0-1 linear programs under objective uncertainty: A completely positive representation, Oper. Res., Volume 59 (2011) no. 3, pp. 713-728 | DOI | MR | Zbl
[286] Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods, Comput. Chem. Eng., Volume 112 (2018), pp. 190-210 | DOI
[287] Stochastic gradient descent: Recent trends, Recent Advances in Optimization and Modeling of Contemporary Problems, INFORMS TutORials in Operations Research, 2018, pp. 193-220 | DOI
[288] Robustifying conditional portfolio decisions via optimal transport, 2021 (https://arxiv.org/abs/2103.16451)
[289] Global unicity in optimization and approximation, Z. Angew. Math. Mech., Volume 65 (1985) no. 5, p. T319-T321 | MR
[290] Global unicity in semi-infinite optimization, Numer. Funct. Anal. Optim., Volume 8 (1985), pp. 173-191 | DOI | MR | Zbl
[291] Empirical likelihood, Chapman & Hall/CRC, 2001
[292] Statistical inference based on divergence measures, Chapman & Hall/CRC, 2005
[293] A Multistage Distributionally Robust Optimization Approach to Water Allocation under Climate Uncertainty (2020) (https://arxiv.org/abs/2005.07811)
[294] Robust Optimization with Ambiguous Stochastic Constraints Under Mean and Dispersion Information, Oper. Res., Volume 66 (2018) no. 3, pp. 814-833 | DOI | MR | Zbl
[295] Data-driven optimization with distributionally robust second-order stochastic dominance constraints, 2020 (Optimization Online http://www.optimization-online.org/DB_HTML/2020/12/8173.html)
[296] Adjustable robust optimization reformulations of two-stage worst-case regret minimization problems, Oper. Res. (2021) (https://doi.org/10.1287/opre.2021.2159) | DOI
[297] Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures, SIAM Rev., Volume 58 (2016) no. 4, pp. 603-650 | DOI | MR | Zbl
[298] Distributionally robust SDDP, Comput. Manag. Sci., Volume 15 (2018) no. 3-4, pp. 431-454 | DOI | MR | Zbl
[299] Simulation optimization: A concise overview and implementation guide, Theory Driven by Influential Applications, INFORMS TutORials in Operations Research, 2013, pp. 122-150
[300] On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach, 2019 (Optimziation Online http://www.optimization-online.org/DB_HTML/2019/01/7043.html)
[301] Evaluations of Risk Measures for Different Probability Measures, SIAM J. Optim., Volume 23 (2013) no. 1, pp. 530-551 | DOI | MR | Zbl
[302] Minimax optimal control of stochastic uncertain systems with relative entropy constraints, IEEE Trans. Autom. Control, Volume 45 (2000) no. 3, pp. 398-412 | DOI | MR | Zbl
[303] A semidefinite programming approach to optimal-moment bounds for convex classes of distributions, Math. Oper. Res., Volume 30 (2005) no. 3, pp. 632-657 | DOI | MR | Zbl
[304] Robust mean-covariance solutions for stochastic optimization, Oper. Res., Volume 55 (2007) no. 1, pp. 98-112 | DOI | MR | Zbl
[305] A distance for multistage stochastic optimization models, SIAM J. Optim., Volume 22 (2012) no. 1, pp. 1-23 | DOI | MR | Zbl
[306] The problem of ambiguity in stochastic optimization, Multistage Stochastic Optimization, Springer, 2014, pp. 229-255
[307] A Review on Ambiguity in Stochastic Portfolio Optimization, Set-Valued Var. Anal., Volume 26 (2018) no. 4, pp. 733-757 | DOI | MR | Zbl
[308] The 1/N investment strategy is optimal under high model ambiguity, J. Bank. Financ., Volume 36 (2012) no. 2, pp. 410-417 | DOI
[309] et al. Bounds for joint portfolios of dependent risks, Stat. Risk Model., Volume 29 (2012) no. 2, pp. 107-132 | DOI | MR | Zbl
[310] Regret in the newsvendor model with partial information, Oper. Res., Volume 56 (2008) no. 1, pp. 188-203 | DOI | MR | Zbl
[311] Computation of sharp bounds on the distribution of a function of dependent risks, J. Comput. Appl. Math., Volume 236 (2012) no. 7, pp. 1833-1840 | DOI | MR | Zbl
[312] Sharp bounds for sums of dependent risks, J. Appl. Probab., Volume 50 (2013) no. 1, pp. 42-53 | DOI | MR | Zbl
[313] An approximation framework for two-stage ambiguous stochastic integer programs under mean-MAD information, Eur. J. Oper. Res., Volume 274 (2019) no. 2, pp. 432-444 | DOI | MR | Zbl
[314] Probabilistic Programming, Stochastic Programming (Ruszczyński, Andrzej; Shapiro, Alexander, eds.) (Handbooks in Operations Research and Management Science), Volume 10, Elsevier, 2003 | DOI | MR
[315] On probabilistic constrained programming, Proceedings of the Princeton symposium on mathematical programming, Princeton University Press (1970), p. 138 | Zbl
[316] Programming under probabilistic constraints with a random technology matrix, Statistics, Volume 5 (1974) no. 2, pp. 109-116 | MR | Zbl
[317] Mathematical foundations of distributionally robust multistage optimization, SIAM J. Optim., Volume 31 (2021) no. 4, pp. 3044-3067 | DOI | MR | Zbl
[318] A survey of the S-lemma, SIAM Rev., Volume 49 (2007) no. 3, pp. 371-418 | DOI | MR | Zbl
[319] Markov decision processes: discrete stochastic dynamic programming, John Wiley & Sons, 2005
[320] Ambiguity in portfolio selection, Quant. Finance, Volume 7 (2007) no. 4, pp. 435-442 | DOI | MR | Zbl
[321] Quantitative stability analysis for minimax distributionally robust risk optimization, Math. Program., Volume 191 (2022), pp. 47-77 | DOI | MR | Zbl
[322] A Composite Risk Measure Framework for Decision Making Under Uncertainty, J. Oper. Res. Soc. China, Volume 7 (2019) no. 1, pp. 43-68 | DOI | MR | Zbl
[323] Probability metrics and the stability of stochastic models, John Wiley & Son Ltd, 1991
[324] Controlling Risk and Demand Ambiguity in Newsvendor Models, Eur. J. Oper. Res., Volume 279 (2019) no. 3, pp. 854-868 | DOI | MR | Zbl
[325] Identifying effective scenarios in distributionally robust stochastic programs with total variation distance, Math. Program., Volume 173 (2019) no. 1–2, pp. 393-430 | DOI | MR | Zbl
[326] Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance, 2021 (to appear in SIAM J. Optim., available on Optimization Online http://www.optimization-online.org/DB_HTML/2021/09/8588.html)
[327] Goodness-of-fit statistics for discrete multivariate data, Springer, 1988 | DOI
[328] Reducing conservatism in robust optimization, INFORMS J. Comput., Volume 32 (2020) no. 4, pp. 1109-1127 | MR | Zbl
[329] Approximate distributions of order statistics: with applications to nonparametric statistics, Springer, 1989 | DOI
[330] Discrete Rényi Classifiers, Advances in Neural Information Processing Systems 28 (Cortes, C.; Lawrence, N. D.; Lee, D. D.; Sugiyama, M.; Garnett, R., eds.), Curran Associates, Inc., 2015, pp. 3276-3284
[331] Numerical methods for semi-infinite programming: A survey, Semi-infinite Programming, Nonconvex Optimization and Its Applications (Reemtsen, R.; Rückmann, J. J., eds.), Kluwer Academic Publishers, 1998, pp. 195-275 | DOI | Zbl
[332] Robust Growth-Optimal Portfolios, Manage. Sci., Volume 62 (2016) no. 7, pp. 2090-2109 | DOI
[333] Chebyshev Inequalities for Products of Random Variables, Math. Oper. Res., Volume 43 (2018) no. 3, pp. 887-918 | DOI | MR | Zbl
[334] Distributionally robust optimization: A review (2019) (https://arxiv.org/abs/1908.05659)
[335] Coherent approaches to risk in optimization under uncertainty, OR Tools and Applications: Glimpses of Future Technologies, INFORMS TutORials in Operations Research, 2007, pp. 38-61
[336] Conjugate Duality and Optimization, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, 1974 | DOI
[337] Convex Analysis, Princeton Landmarks in Mathematics, Princeton University Press, 1997
[338] Quantitative stability in stochastic programming: The method of probability metrics, Math. Oper. Res., Volume 27 (2002) no. 4, pp. 792-818 | DOI | MR | Zbl
[339] Measures of residual risk with connections to regression, risk tracking, surrogate models, and ambiguity, SIAM J. Optim., Volume 25 (2015) no. 2, pp. 1179-1208 | DOI | MR | Zbl
[340] Mass Transportation Problems: Volume I: Theory, Springer, 1998
[341] Robust Conic Satisficing, 2021 (https://arxiv.org/abs/2107.06714)
[342] Optimization of convex risk functions, Math. Oper. Res., Volume 31 (2006) no. 3, pp. 433-452 | DOI | MR | Zbl
[343] Scenario reduction revisited: fundamental limits and guarantees, Math. Program., Volume 191 (2022), pp. 207-242 | DOI | MR | Zbl
[344] Optimization of conditional value-at-risk, J. Risk, Volume 2 (2000), pp. 21-42 | DOI
[345] Conditional value-at-risk for general loss distributions, J. Bank. Financ., Volume 26 (2002) no. 7, pp. 1443-1471 | DOI
[346] Nonlinear optimization, Princeton University Press, 2006 | DOI
[347] Variational theory for optimization under stochastic ambiguity, SIAM J. Optim., Volume 27 (2017) no. 2, pp. 1118-1149 | DOI | MR | Zbl
[348] Stability of Stochastic Programming Problems, Stochastic Programming (Ruszczyński, Andrzej; Shapiro, Alexander, eds.) (Handbooks in Operations Research and Management Science), Volume 10, Elsevier, 2003, pp. 483-554 | DOI | MR
[349] On a class of minimax stochastic programs, SIAM J. Optim., Volume 14 (2004) no. 4, pp. 1237-1249 | DOI | MR | Zbl
[350] Distributionally Robust Logistic Regression, Advances in Neural Information Processing Systems 28 (Cortes, C.; Lawrence, N. D.; Lee, D. D.; Sugiyama, M.; Garnett, R., eds.), Curran Associates, Inc., 2015, pp. 1576-1584
[351] Regularization via Mass Transportation., J. Mach. Learn. Res., Volume 20 (2019) no. 103, pp. 1-68 | MR | Zbl
[352] Wasserstein Distributionally Robust Kalman Filtering, Advances in Neural Information Processing Systems (Bengio, S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R., eds.), Curran Associates, Inc. (2018), pp. 8474-8483
[353] The theory of statistical decision, J. Am. Stat. Assoc., Volume 46 (1951) no. 253, pp. 55-67 | DOI | Zbl
[354] A min-max solution of an inventory problem, Studies in the mathematical theory of inventory and production (Scarf, Herbert; Arrow, KJ; Karlin, S, eds.), Stanford University Press, Stanford, CA, 1958, pp. 201-209
[355] Some aspects of stability in stochastic programming, Ann. Oper. Res., Volume 100 (2000) no. 1-4, pp. 55-84 | DOI | MR | Zbl
[356] Distributionally robust reinforcement learning, 2019 (https://arxiv.org/abs/1902.08708)
[357] Lectures on stochastic programming: modeling and theory, MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics, 2014
[358] On the empirical estimation of integral probability metrics, Electron. J. Stat., Volume 6 (2012), pp. 1550-1599 | MR | Zbl
[359] A Hilbert space embedding for distributions, 18th International Conference on Algorithmic Learning Theory (Hutter, Marcus; Servedio, Rocco A.; Takimoto, Eiji, eds.), Springer (2007), pp. 13-31 | DOI | Zbl
[360] K-adaptability in two-stage mixed-integer robust optimization, Math. Program. Comput., Volume 12 (2020) no. 2, pp. 193-224 | DOI | MR | Zbl
[361] On Duality Theory of Conic Linear Problems, Semi-Infinite Programming: Recent Advances (Goberna, Miguel Á.; López, Marco A., eds.), Springer, 2001, pp. 135-165 | DOI | Zbl
[362] Minimax and risk averse multistage stochastic programming, Eur. J. Oper. Res., Volume 219 (2012) no. 3, pp. 719-726 | DOI | MR | Zbl
[363] On Kusuoka representation of law invariant risk measures, Math. Oper. Res., Volume 38 (2013) no. 1, pp. 142-152 | DOI | MR | Zbl
[364] Rectangular sets of probability measures, Oper. Res., Volume 64 (2016) no. 2, pp. 528-541 | DOI | MR | Zbl
[365] Distributionally robust stochastic programming, SIAM J. Optim., Volume 27 (2017) no. 4, pp. 2258-2275 | DOI | MR | Zbl
[366] Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming, Eur. J. Oper. Res., Volume 288 (2021) no. 1, pp. 1-13 | DOI | MR | Zbl
[367] Data-driven robust optimization based on kernel learning, Comput. Chem. Eng., Volume 106 (2017), pp. 464-479 | DOI
[368] On general minimax theorems, Pac. J. Math., Volume 8 (1958) no. 1, pp. 171-176 | DOI | MR | Zbl
[369] Distributionally robust deep learning as a generalization of adversarial training, NIPS workshop on Machine Learning and Computer Security, Volume 1 (2017)
[370] Distributionally Robust Optimization and Generalization in Kernel Methods, Advances in Neural Information Processing Systems (Wallach, H.; Larochelle, H.; Beygelzimer, A.; Alché-Buc, F. d; Fox, E.; Garnett, R., eds.), Volume 32, Curran Associates, Inc. (2019)
[371] Minimax analysis of stochastic problems, Optim. Methods Softw., Volume 17 (2002) no. 3, pp. 523-542 | DOI | MR | Zbl
[372] Quadratic two-stage stochastic optimization with coherent measures of risk, Math. Program., Volume 168 (2018) no. 1-2, pp. 599-613 | DOI | MR | Zbl
[373] Generalized Chebychev inequalities: theory and applications in decision analysis, Oper. Res., Volume 43 (1995) no. 5, pp. 807-825 | DOI | MR | Zbl
[374] On Complexity of Stochastic Programming Problems, Continuous Optimization: Current Trends and Modern Applications (Jeyakumar, Vaithilingam; Rubinov, Alexander, eds.), Springer, 2005, pp. 111-146 | DOI | Zbl
[375] On complexity of stochastic programming problems, Continuous Optimization: Current Trends and Modern Applications (Jeyakumar, Vaithilingam; Rubinov, Alexander, eds.), Springer, 2005, pp. 111-146 | DOI | Zbl
[376] Certifying Some Distributional Robustness with Principled Adversarial Training, 2018 (https://arxiv.org/abs/1710.10571)
[377] Minimax Distribution Estimation in Wasserstein Distance, 2018 (https://arxiv.org/abs/1802.08855)
[378] Learning with kernels: support vector machines, regularization, optimization, and beyond, MIT Press, 2002
[379] Robust approximation to multiperiod inventory management, Oper. Res., Volume 58 (2010) no. 3, pp. 583-594 | MR | Zbl
[380] PICOS: A Python interface to conic optimization solvers, J. Open Source Softw., Volume 7 (2022) no. 70, p. 3915 | DOI
[381] Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, 2014
[382] On the influence of the kernel on the consistency of support vector machines, J. Mach. Learn. Res., Volume 2 (2001) no. Nov, pp. 67-93 | MR | Zbl
[383] Generalized semi-infinite programming: theory and methods, Eur. J. Oper. Res., Volume 119 (1999), pp. 301-313 | DOI | Zbl
[384] Worst-case-expectation approach to optimization under uncertainty, Oper. Res., Volume 61 (2013) no. 6, pp. 1435-1449 | DOI | MR | Zbl
[385] The analytics of robust satisficing, 2021 (available at SSRN 3829562)
[386] A general framework for optimal data-driven optimization, 2020 (https://arxiv.org/abs/2010.06606)
[387] Distributionally robust optimization for planning and scheduling under uncertainty, Comput. Chem. Eng., Volume 110 (2018), pp. 53-68 | DOI
[388] Robust Optimization in High-Dimensional Data Space with Support Vector Clustering, IFAC-PapersOnLine, Volume 51 (2018) no. 18, pp. 19-24 | DOI
[389] A data-driven robust optimization approach to scenario-based stochastic model predictive control, J. Process Control, Volume 75 (2019), pp. 24-39 | DOI
[390] Large margin methods for structured and interdependent output variables, J. Mach. Learn. Res., Volume 6 (2005) no. Sep, pp. 1453-1484 | MR | Zbl
[391] Machine learning with operational costs, J. Mach. Learn. Res., Volume 14 (2013) no. 1, pp. 1989-2028 | MR | Zbl
[392] On combining machine learning with decision making, Mach. Learn., Volume 97 (2014) no. 1-2, pp. 33-64 | DOI | MR | Zbl
[393] Robust optimization using machine learning for uncertainty sets, 2014 (https://arxiv.org/abs/1407.1097)
[394] Theory of statistical inference and information, Kluwer Academic Publishers, 1989
[395] Efficient Data-Driven Optimization with Noisy Data, 2021 (https://arxiv.org/abs/2102.04363)
[396] Generalized Chebyshev bounds via semidefinite programming, SIAM Rev., Volume 49 (2007) no. 1, pp. 52-64 | DOI | MR | Zbl
[397] Optimal transport: old and new, Springer, 2008
[398] ROC++: Robust Optimization in C++, 2020 (https://arxiv.org/abs/2006.08741)
[399] From data to decisions: Distributionally robust optimization is optimal, Manage. Sci., Volume 67 (2021) no. 6, pp. 3387-3402 | DOI
[400] Generalized Gauss inequalities via semidefinite programming, Math. Program., Volume 156 (2016) no. 1, pp. 271-302 | DOI | MR | Zbl
[401] Distributionally robust expectation inequalities for structured distributions, Math. Program., Volume 173 (2019) no. 1-2, pp. 251-280 | DOI | MR | Zbl
[402] Distributionally Robust Control of Constrained Stochastic Systems, IEEE Trans. Autom. Control, Volume 61 (2016) no. 2, pp. 430-442 | MR | Zbl
[403] Stochastic Optimization Using Hellinger Distance, Proceedings of the 2015 Winter Simulation Conference (WSC ’15) (2015), pp. 3702-3713 | DOI
[404] Likelihood robust optimization for data-driven problems, Comput. Manag. Sci., Volume 13 (2016) no. 2, pp. 241-261 | DOI | MR | Zbl
[405] Robust Markov Decision Processes, Math. Oper. Res., Volume 38 (2013) no. 1, pp. 153-183 | DOI | MR | Zbl
[406] Distributionally robust convex optimization, Oper. Res., Volume 62 (2014) no. 6, pp. 1358-1376 | DOI | MR | Zbl
[407] A Solution Approach to Distributionally Robust Joint-Chance-Constrained Assignment Problems, INFORMS J. Optim. (2022) (https://doi.org/10.1287/ijoo.2021.0060) | MR
[408] ROmodel: modeling robust optimization problems in Pyomo, Optim. Eng. (2021) (https://doi.org/10.1007/s11081-021-09703-2)
[409] A framework for optimization under ambiguity, Ann. Oper. Res., Volume 193 (2012) no. 1, pp. 21-47 | DOI | MR | Zbl
[410] Robustifying Convex Risk Measures for Linear Portfolios: A Nonparametric Approach, Oper. Res., Volume 62 (2014) no. 6, pp. 1302-1315 | DOI | MR | Zbl
[411] The complete mixability and convex minimization problems with monotone marginal densities, J. Multivariate Anal., Volume 102 (2011) no. 10, pp. 1344-1360 | DOI | MR | Zbl
[412] Feasible method for semi-infinite programs, SIAM J. Optim., Volume 25 (2015) no. 4, pp. 2537-2560 | DOI | MR | Zbl
[413] Distributionally robust simple integer recourse, Comput. Manag. Sci., Volume 15 (2018) no. 3, pp. 351-367 | MR | Zbl
[414] On Deterministic Reformulations of Distributionally Robust Joint Chance Constrained Optimization Problems, SIAM J. Optim., Volume 28 (2018) no. 2, pp. 1151-1182 | MR | Zbl
[415] Optimized Bonferroni approximations of distributionally robust joint chance constraints, Math. Program., Volume 191 (2022), pp. 79-112 | MR | Zbl
[416] A data-driven distributionally robust bound on the expected optimal value of uncertain mixed 0-1 linear programming, Comput. Manag. Sci., Volume 15 (2018) no. 1, pp. 111-134 | MR | Zbl
[417] Robustness and regularization of support vector machines, J. Mach. Learn. Res., Volume 10 (2009) no. Jul, pp. 1485-1510 | MR | Zbl
[418] Optimization under probabilistic envelope constraints, Oper. Res., Volume 60 (2012) no. 3, pp. 682-699 | MR | Zbl
[419] Time (in) consistency of multistage distributionally robust inventory models with moment constraints, Eur. J. Oper. Res. (2021), pp. 1127-1141 | MR | Zbl
[420] Distributionally robust inventory control when demand is a martingale, Math. Oper. Res. (2022) (https://doi.org/10.1287/moor.2021.1213)
[421] Tractable reformulations of two-stage distributionally robust linear programs over the type- Wasserstein ball, Oper. Res. Lett., Volume 48 (2020) no. 4, pp. 513-523 | MR | Zbl
[422] On distributionally robust chance constrained programs with Wasserstein distance, Math. Program., Volume 186 (2021) no. 1, pp. 115-155 | MR | Zbl
[423] Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods, Math. Program., Volume 169 (2018) no. 2, pp. 489-529 | MR | Zbl
[424] Distributionally Robust Markov Decision Processes, Advances in Neural Information Processing Systems 23 (Lafferty, J. D.; Williams, C. K. I.; Shawe-Taylor, J.; Zemel, R. S.; Culotta, A., eds.), Curran Associates, Inc., 2010, pp. 2505-2513
[425] Distributionally Robust Markov Decision Processes, Math. Oper. Res., Volume 37 (2012) no. 2, pp. 288-300 | MR | Zbl
[426] Solving semi-infinite programs by smoothing projected gradient method, Comput. Math. Appl., Volume 59 (2014) no. 3, pp. 591-616 | MR | Zbl
[427] A dynamic game approach to distributionally robust safety specifications for stochastic systems, Automatica, Volume 94 (2018), pp. 94-101 | DOI | MR | Zbl
[428] Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approach, IEEE Trans. Autom. Control (2020) | MR | Zbl
[429] Expected value of distribution information for the newsvendor problem, Oper. Res., Volume 54 (2006) no. 6, pp. 1128-1136 | MR | Zbl
[430] Optimality conditions for semi-infinite and generalized semi-infinite programs via lower order exact penalty functions, J. Optim. Theory Appl., Volume 169 (2016) no. 3, pp. 984-1012 | DOI | MR | Zbl
[431] Safe approximations of ambiguous chance constraints using historical data, INFORMS J. Comput., Volume 25 (2012) no. 4, pp. 666-681 | DOI | MR
[432] A survey of adjustable robust optimization, Eur. J. Oper. Res., Volume 277 (2019) no. 3, pp. 799-813 | DOI | MR | Zbl
[433] Multistage Distributionally Robust Mixed-Integer Programming with Decision-Dependent Moment-Based Ambiguity Sets, Math. Program. (2020) | DOI
[434] Distributionally robust counterpart in Markov decision processes, IEEE Trans. Autom. Control, Volume 61 (2016) no. 9, pp. 2538-2543 | MR | Zbl
[435] Distributionally robust chance constraints for non-linear uncertainties, Math. Program., Volume 155 (2016) no. 1-2, pp. 231-265 | DOI | MR | Zbl
[436] Robust Optimization for the Loss-Averse Newsvendor Problem, J. Optim. Theory Appl., Volume 171 (2016) no. 3, pp. 1008-1032 | DOI | MR | Zbl
[437] Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support, SIAM J. Optim., Volume 31 (2021) no. 3, pp. 1690-1721 | DOI | MR | Zbl
[438] Adjustable Robust Optimization via Fourier-Motzkin Elimination, Oper. Res., Volume 66 (2018) no. 4, pp. 1086-1100 | DOI | MR | Zbl
[439] Branch and price for chance-constrained bin packing, INFORMS J. Comput., Volume 32 (2020) no. 3, pp. 547-564 | DOI | MR | Zbl
[440] Data-Driven Risk-Averse Two-Stage Stochastic Program with -Structure Probability Metrics, 2015 (Optimization Online http://www.optimization-online.org/DB_HTML/2015/07/5014.html)
[441] Data-driven risk-averse stochastic optimization with Wasserstein metric, Oper. Res. Lett., Volume 46 (2018) no. 2, pp. 262-267 | DOI | MR | Zbl
[442] Distributionally robust contingency-constrained unit commitment, IEEE Trans. Power Syst., Volume 33 (2018) no. 1, pp. 94-102 | DOI
[443] Kernel Distributionally Robust Optimization: Generalized Duality Theorem and Stochastic Approximation, International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research (2021), pp. 280-288
[444] Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information, SIAM J. Optim., Volume 28 (2018) no. 4, pp. 2922-2944 | DOI | MR | Zbl
[445] Distributionally robust joint chance constraints with second-order moment information, Math. Program., Volume 137 (2013) no. 1, pp. 167-198 | DOI | MR | Zbl
[446] Worst-Case Value at Risk of Nonlinear Portfolios, Manage. Sci., Volume 59 (2013) no. 1, pp. 172-188 | DOI
[447] Quantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints, SIAM J. Optim., Volume 26 (2016) no. 3, pp. 1855-1882 | DOI | MR | Zbl
[448] Finite-Sample Regret Bound for Distributionally Robust Offline Tabular Reinforcement Learning, International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research (2021), pp. 3331-3339
[449] On minimax solutions of stochastic linear programming problems, Časopis pro pěstováná matematiky, Volume 091 (1966) no. 4, pp. 423-430 | DOI | MR
Cité par Sources :
