Optimality Conditions for Nonsmooth Equilibrium Problems via Hadamard Directional Derivative

被引：3

作者：

Ardali, A. Ansari ^{[1
]}

Movahedian, N. ^{[1
]}

Nobakhtian, S. ^{[1
,2
]}

机构：

[1] Univ Isfahan, Dept Math, POB 81745-163, Esfahan, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2016年 / 24卷 / 03期

关键词：

Equilibrium problems; Optimality conditions; Constraint qualifications; Hadamard directional derivative; VARIATIONAL INEQUALITY CONSTRAINTS; MATHEMATICAL PROGRAMS; OPTIMIZATION PROBLEMS; SUFFICIENT CONDITIONS;

D O I：

10.1007/s11228-015-0354-3

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. We obtain necessary conditions of Fritz John (FJ) and Karush-Kuhn-Tucker (KKT) types for a nonsmooth (MPEC) problem in terms of the lower Hadamard directional derivative. In particular sufficient conditions for MPECs are given where the involved functions have pseudoconvex sublevel sets. The functions with pseudoconvex sublevel sets is a class of generalized convex functions that include quasiconvex functions.

引用

页码：483 / 497

页数：15

共 18 条

[1] Quasiconvex programming with locally starshaped constraint region and applications to quasiconvex MPEC
Aussel, D.
Ye, J. J.
[J]. OPTIMIZATION, 2006, 55 (5-6) : 433 - 457
[2] Bazaraa M. S., 2006, NONLINEAR PROGRAMMIN
[3] KKT REFORMULATION AND NECESSARY CONDITIONS FOR OPTIMALITY IN NONSMOOTH BILEVEL OPTIMIZATION
Dempe, Stephan
Zemkoho, Alain B.
[J]. SIAM JOURNAL ON OPTIMIZATION, 2014, 24 (04) : 1639 - 1669
[4] Demyanov VF., 1995, Constructive nonsmooth analysis
[5] On M-stationary points for mathematical programs with equilibrium constraints
Flegel, ML
Kanzow, C
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 310 (01) : 286 - 302
[6] Abadie-type constraint qualification for mathematical programs with equilibrium constraints
Flegel, ML
Kanzow, C
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 124 (03) : 595 - 614
[7] A FRITZ-JOHN OPTIMALITY CONDITION USING THE APPROXIMATE SUBDIFFERENTIAL
GLOVER, BM
CRAVEN, BD
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1994, 82 (02) : 253 - 265
[8] On the functions with pseudoconvex sublevel sets and optimality conditions
Ivanov, Vsevolod I.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (02) : 964 - 974
[9] GENERALIZED DIFFERENTIAL-CALCULUS FOR NONSMOOTH AND SET-VALUED MAPPINGS
MORDUKHOVICH, BS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 183 (01) : 250 - 288
[10] Necessary and sufficient conditions for nonsmooth mathematical programs with equilibrium constraints
Movahedian, N.
Nobakhtian, S.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (05) : 2694 - 2705

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