Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

被引：45

作者：

Guo, Lei ^{[1
]}

Lin, Gui-Hua ^{[2
]}

Ye, Jane J. ^{[3
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[2] Shanghai Univ, Sch Management, Shanghai 200444, Peoples R China

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

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2013年 / 158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; Second-order optimality condition; Constraint qualification; Isolatedness; VARIATIONAL INEQUALITY CONSTRAINTS; LINEAR-DEPENDENCE CONDITION; COMPLEMENTARITY CONSTRAINTS; OPTIMIZATION PROBLEMS; GENERALIZED EQUATIONS; EXACT PENALIZATION; ORDER CONDITIONS; SQP METHODS; CONVERGENCE; QUALIFICATIONS;

D O I：

10.1007/s10957-012-0228-x

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：

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second-order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions.

引用

页码：33 / 64

页数：32

共 48 条

[41] Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity [J].

Scheel, H ;

Scholtes, S .

MATHEMATICS OF OPERATIONS RESEARCH, 2000, 25 (01) :1-22

[42] Convergence properties of a regularization scheme for mathematical programs with complementarity constraints [J].

Scholtes, S .

SIAM JOURNAL ON OPTIMIZATION, 2001, 11 (04) :918-936

[43]

Ye J.J., J OPTIM THE IN PRESS

[44] Necessary optimality conditions for optimization problems with variational inequality constraints [J].

Ye, JJ ;

Ye, XY .

MATHEMATICS OF OPERATIONS RESEARCH, 1997, 22 (04) :977-997

[45] Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints [J].

Ye, JJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 307 (01) :350-369

[46] Exact penalization and necessary optimality conditions for generalized bilevel programming problems [J].

Ye, JJ ;

Zhu, DL ;

Zhu, QJ .

SIAM JOURNAL ON OPTIMIZATION, 1997, 7 (02) :481-507

[47] Optimality conditions for optimization problems with complementarity constraints [J].

Ye, JJ .

SIAM JOURNAL ON OPTIMIZATION, 1999, 9 (02) :374-387

[48] Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints [J].

Ye, JJ .

SIAM JOURNAL ON OPTIMIZATION, 2000, 10 (04) :943-962

← 1 2 3 4 5 →