SUBOPTIMALITY CONDITIONS FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS

作     者：Bao, Truong Q. Gupta, Pankaj Mordulchovich, Boris S. 

作者机构：Wayne State Univ Dept Math Detroit MI 48202 USA Univ Delhi Dept Operat Res Delhi 110007 India 

出 版 物：《TAIWANESE JOURNAL OF MATHEMATICS》 (Taiwanese J. Math.)

年 卷 期：2008年第12卷第9期

页      面：2569-2592页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：US National Science Foundation [DMS-0304989, DMS-0603846] Indian BOYSCAST Fellowship Australian Research Council [DP-04511668] 

主　　题：Mathematical programs with equilibrium constraints Variational analysis Nonsmooth optimization Extremal principle Subdifferential variational principle Generalized differentiation Coderivatives 

摘      要：In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended form 0 is an element of G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish new weak and strong suboptimality conditions for the general MPEC problems under consideration in finite-dimensional and infinite-dimensional spaces that do not assume the existence of optimal solutions. This issue is particularly important for infinite-dimensional optimization problems, where the existence of optimal solutions requires quite restrictive assumptions. Our techniques are mainly based on modem tools of variational analysis and generalized differentiation revolving around the fundamental extremal principle in variational analysis and its analytic counterpart known as the subdifferential variational principle.