Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints

被引：193

作者：

Ye, JJ ^{[1
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2005年 / 307卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

mathematical program with equilibrium constraints; necessary optimality conditions; sufficient optimality conditions; constraint qualifications;

D O I：

10.1016/j.jmaa.2004.10.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient for global or local optimality under some MPEC generalized convexity assumptions. Moreover, we propose new constraint qualifications for M-stationary conditions to hold. These new constraint qualifications include piecewise MFCQ, piecewise Slater condition, MPEC weak reverse convex constraint qualification, MPEC Arrow-Hurwicz-Uzawa constraint qualification, MPEC Zangwill constraint qualification, MPEC Kuhn-Tucker constraint qualification, and MPEC Abadie constraint qualification. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：350 / 369

页数：20

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