In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.
Accepté le :
DOI : 10.1051/ro/2017054
Mots-clés : Nonmonotone technique, conic model, line search, trust region, bound constrained optimization
@article{RO_2019__53_3_787_0,
author = {Zhao, Lijuan},
title = {Nonmonotone conic trust region method with line search technique for bound constrained optimization},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {787--805},
publisher = {EDP-Sciences},
volume = {53},
number = {3},
year = {2019},
doi = {10.1051/ro/2017054},
mrnumber = {3973144},
zbl = {1461.65192},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2017054/}
}
TY - JOUR AU - Zhao, Lijuan TI - Nonmonotone conic trust region method with line search technique for bound constrained optimization JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 787 EP - 805 VL - 53 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2017054/ DO - 10.1051/ro/2017054 LA - en ID - RO_2019__53_3_787_0 ER -
%0 Journal Article %A Zhao, Lijuan %T Nonmonotone conic trust region method with line search technique for bound constrained optimization %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 787-805 %V 53 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2017054/ %R 10.1051/ro/2017054 %G en %F RO_2019__53_3_787_0
Zhao, Lijuan. Nonmonotone conic trust region method with line search technique for bound constrained optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 3, pp. 787-805. doi : 10.1051/ro/2017054. http://archive.numdam.org/articles/10.1051/ro/2017054/
, and , Constrained dogleg methods for nonlinear systems with simple bounds. Comput. Optimiz. Appl. 53 (2012) 771–794. | DOI | MR | Zbl
, and , An affine scaling trust-region approach to bound-constrained nonlinear systems. Appl. Numer. Math. 44 (2003) 257–280. | DOI | MR | Zbl
and , On affine scaling inexact dogleg methods for bound constrained nonlinear systems. Optimiz. Methods Software 30 (2015) 276–300. | DOI | MR | Zbl
and , An interior trust-region approach for minimization subject to bounds. SIAM J. Optimiz. 6 (1996) 418–445. | DOI | MR | Zbl
, and , Testing a class of methods for solving minimization problems with simple bounds on the variables. Math. Comput. 50 (1988) 399–430. | DOI | MR | Zbl
, and , Combining nonmonotone conic trust region and line search techniques for unconstrained optimization. J. Comput. Appl. Math. 235 (2011) 2432–2441. | DOI | MR | Zbl
, Conic approximations and collinear scalings for optimizers. SIAM J. Numer. Anal. 17 (1980) 268–281. | DOI | MR | Zbl
and , A trust region method for conic model to solve unconstrained optimizations. Optimiz. Methods and Software 6 (1996) 237–263. | DOI
and , Nonmonotone adaptive trust-region method for unconstrained optimization problems. Appl. Math. Comput. 163 (2005) 489–504. | MR | Zbl
and , Benchmarking optimization software performance profiles. Math. Program. 91 (2002) 201–213. | DOI | MR | Zbl
, and , A nonmonotone line search technique for Newton’s method. SIAM J. Numer. Anal. 23 (1986) 707–716. | DOI | MR | Zbl
and , Incorporating nonmonotone strategies into the trust region method for unconstrained optimization. Comput. Math. Appl. 55 (2008) 2158–2172. | DOI | MR | Zbl
, and , Superlinear and quadratic convergence of affine scaling interior point Newton methods for problems with simple bounds without strict complementarity assumption. Math. Program. 86 (1999) 615–635. | DOI | MR | Zbl
and , Test examples for nonlinear programming codes, Springer (1981). | DOI | MR
, and , An affine scaling interior point CBB method for box constrained optimization. Math. Program. 119 (2009) 1–32. | DOI | MR | Zbl
and , An affine scaling method for optimization with polyhedral constraints. Comput. Optimiz. Appl. 59 (2014) 163–183. | DOI | MR | Zbl
, , and , A new nonmonotone trust region method of conic model for solving unconstrained optimization. J. Comput. Appl. Math. 233 (2010) 1746–1754. | DOI | MR | Zbl
and , On affine scaling interior point Newton methods for nonlinear minimization with bound constraints. Comput. Optimiz. Appl. 35 (2006) 177–197. | DOI | MR | Zbl
and , Numerical Optimization. Springer, New York (1999). | DOI | MR | Zbl
and , Combining trust region and line search techniques, edited by . Advances in Nonlinear Programming, Kluwer Academic Publishers, Dordrecht (1996) 153–175. | MR | Zbl
, Optimality conditions for trust region subproblems involving a conic model. SIAM J. Optimiz. 15 (2005) 826–837. | DOI | MR | Zbl
and , A trust region method with a conic model for unconstrained optimization. Math. Methods Appl. Sci. 31 (2008) 1780–1808. | DOI | MR | Zbl
and , Optimization Theory and Methods: Nonlinear Programming, Vol 1 of Springer Optimization and its Applications, Springer, New York (2006). | Zbl
, Nonmonotone trust region method for solving optimization problems. Appl. Math. Comput. 156 (2004) 159–174. | MR | Zbl
, The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization. SIAM J. Numer. Anal. 17 (1980) 84–114. | DOI | MR | Zbl
, Exact two steps SOCP/SDP formulation for a modified conic trust region subproblem. Optimiz. Lett. 11 (2017) 1691–1697. | DOI | MR | Zbl
, An iterative algorithm for the conic trust region subproblem. Inter. J. Appl. Comput. Math. 3 (2017) 2553–2558. | DOI | MR | Zbl
, A nonmonotone trust region algorithm for nonlinear optimization subject to convex constraints. Math. Program. 77 (1997) 69–94. | DOI | MR | Zbl
, A trust-region affine scaling method for bound constrained optimization. Acta Math. Sci. 29 (2013) 159–182. | MR | Zbl
, Solving bound constrained optimization via a new nonmonotone spectral projected gradient method. Appl. Numer. Math. 58 (2008) 1340–1348. | DOI | MR | Zbl
and , A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optimiz. 14 (2004) 1043–1056. | DOI | MR | Zbl
and , A conic affine scaling dogleg method for nonlinear optimization with bound constraints. Asia-Pacific J. Operat. Res. 30 (2013) 1–30. | MR | Zbl
, Affine scaling inexact generalized Newton algorithm with interior backtracking technique for solving bound-constrained semismooth equations. J. Comput. Appl. Math. 187 (2006) 227–252. | DOI | MR | Zbl
, An affine scaling trust-region algorithm with interior backtracking technique for solving bound-constrained nonlinear systems. J. Comput. Appl. Math. 184 (2005) 343–361. | DOI | MR | Zbl
, An interior affine scaling projective algorithm for nonlinear equality and linear inequality constrained optimization. J. Comput. Appl. Math. 173 (2005) 115–148. | DOI | MR | Zbl
, Affine scaling interior Levenberg-Marquardt method for bound-constrained semismooth equations under local error bound conditions. J. Comput. Appl. Math. 219 (2008) 198–215. | DOI | MR | Zbl
Cité par Sources :
