Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints

被引：7

作者：

Kohli, Bhawna ^{[1
]}

机构：

[1] Univ Delhi, PGDAV Coll, Dept Math, Delhi 110065, India

来源：

RAIRO-OPERATIONS RESEARCH | 2019年 / 53卷 / 05期

关键词：

Mathematical programs with equilibrium constraints; Convexifactors; Guignard constraint qualification; Strong stationarity; Optimality conditions; OPTIMIZATION PROBLEMS; GENERALIZED CONVEXITY; DUALITY; QUALIFICATIONS; STATIONARITY; TERMS;

D O I：

10.1051/ro/2018084

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The main aim of this paper is to develop necessary Optimality conditions using Convexifactors for mathematical programs with equilibrium constraints (MPEC). For this purpose a nonsmooth version of the standard Guignard constraint qualification (GCQ) and strong stationarity are introduced in terms of convexifactors for MPEC. It is shown that Strong stationarity is the first order necessary optimality condition under nonsmooth version of the standard GCQ. Finally, notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are used to establish the sufficient optimality conditions for MPEC.

引用

页码：1617 / 1632

页数：16

共 50 条

[41] Sufficient Conditions for the Krotov Optimality: Are They Necessary?
Dmitruk, A. V.
[J]. Automation and Remote Control (English translation of Avtomatika i Telemekhanika), 58 (01):
[42] Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications
Achtziger, Wolfgang
Kanzow, Christian
[J]. MATHEMATICAL PROGRAMMING, 2008, 114 (01) : 69 - 99
[43] FIRST-ORDER OPTIMALITY CONDITIONS FOR ELLIPTIC MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS VIA VARIATIONAL ANALYSIS
Hintermueller, M.
Surowiec, T.
[J]. SIAM JOURNAL ON OPTIMIZATION, 2011, 21 (04) : 1561 - 1593
[44] Necessary and sufficient optimality conditions for nonsmooth nonconvex generalized Nash equilibrium problems
Ghasemi, A.
Movahedian, N.
[J]. OPTIMIZATION, 2024,
[45] Necessary and sufficient conditions for optimality of nonconvex, noncoercive autonomous variational problems with constraints
Marcelli, Cristina
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (10) : 5201 - 5227
[46] SUFFICIENT OPTIMALITY CONDITIONS FOR GLOBAL PARETO SOLUTIONS TO MULTIOBJECTIVE PROBLEMS WITH EQUILIBRIUM CONSTRAINTS
Bao, Truong Q.
Mordukhovich, Boris S.
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2014, 15 (01) : 105 - 127
[47] Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints
Z. Y. Wu
V. Jeyakumar
A. M. Rubinov
[J]. Journal of Optimization Theory and Applications, 2007, 133 : 123 - 130
[48] Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints
Wu, Z. Y.
Jeyakumar, V.
Rubinov, A. M.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2007, 133 (01) : 123 - 130
[49] A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints
Ademir A. Ribeiro
Mael Sachine
Evelin H. M. Krulikovski
[J]. Journal of Optimization Theory and Applications, 2022, 192 : 1067 - 1083
[50] Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method
Izmailov, A. F.
Solodov, M. V.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 142 (03) : 501 - 532

← 1 2 3 4 5 →