In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions.
Mots-clés : stochastic mathematical program with equilibrium constraints, S-stationarity, Mangasarian-Fromovitz constraint qualification
@article{COCV_2005__11_2_252_0,
author = {Lin, Gui-Hua and Fukushima, Masao},
title = {Regularization method for stochastic mathematical programs with complementarity constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {252--265},
publisher = {EDP-Sciences},
volume = {11},
number = {2},
year = {2005},
doi = {10.1051/cocv:2005005},
mrnumber = {2141889},
zbl = {1080.90055},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2005005/}
}
TY - JOUR AU - Lin, Gui-Hua AU - Fukushima, Masao TI - Regularization method for stochastic mathematical programs with complementarity constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 252 EP - 265 VL - 11 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2005005/ DO - 10.1051/cocv:2005005 LA - en ID - COCV_2005__11_2_252_0 ER -
%0 Journal Article %A Lin, Gui-Hua %A Fukushima, Masao %T Regularization method for stochastic mathematical programs with complementarity constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 252-265 %V 11 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2005005/ %R 10.1051/cocv:2005005 %G en %F COCV_2005__11_2_252_0
Lin, Gui-Hua; Fukushima, Masao. Regularization method for stochastic mathematical programs with complementarity constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 252-265. doi : 10.1051/cocv:2005005. http://archive.numdam.org/articles/10.1051/cocv:2005005/
[1] and, Introduction to Stochastic Programming. Springer, New York (1997). | MR | Zbl
[2] and, Optimization problems with perturbations: A guided tour. SIAM Rev. 40 (1998) 228-264. | Zbl
[3] and, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions. Optimization 32 (1995) 193-209. | Zbl
[4] , and, The Linear Complementarity Problem. Academic Press, New York, NY (1992). | MR | Zbl
[5] , Solution point differentiability without strict complementarity in nonlinear programming. Math. Program. Stud. 21 (1984) 127-138. | Zbl
[6] and, Stochastic Programming. John Wiley & Sons, Chichester (1994). | MR | Zbl
[7] , and, Smoothing implicit programming approaches for stochastic mathematical programs with linear complementarity constraints. Technical Report 2003-006, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan (2003).
[8] and, A class of stochastic mathematical programs with complementarity constraints: Reformulations and algorithms. Technical Report 2003-010, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan (2003).
[9] , and, Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK (1996). | MR | Zbl
[10] , Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992). | MR | Zbl
[11] and, Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. 25 (1999) 159-167. | Zbl
[12] and, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25 (2000) 1-22. | Zbl
Cité par Sources :
