Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity

被引：499

作者：

Scheel, H ^{[1
]}

Scholtes, S

机构：

[1] Univ Dortmund, D-44221 Dortmund, Germany

[2] Univ Cambridge, Judge Inst Management Studies, Cambridge CB2 1AG, England

[3] Univ Cambridge, Dept Engn, Cambridge CB2 1AG, England

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2000年 / 25卷 / 01期

关键词：

Bouligand stationarity; Clarke stationarity; vertical complementarity constraints; equilibrium constraints; exact penalty function; sensitivity; stability; strong stationarity; weak stationarity;

D O I：

10.1287/moor.25.1.1.15213

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 mathematical programs with complementarity constraints. Several stationarity concepts, based on a piecewise smooth formulation, are presented and compared. The concepts are related to stationarity conditions for certain smooth programs as well as to stationarity concepts for a nonsmooth exact penalty function. Further, we present Fiacco-McCormick type second order optimality conditions and an extension of the stability results of Robinson and Kojima to mathematical programs with complementarity constraints.

引用

页码：1 / 22

页数：22

共 31 条

[1]

BURKE JV, 1991, SIAM J CONTROL OPTIM, V29, P1340

[2] BILEVEL PROGRAMMING FOR STEADY-STATE CHEMICAL PROCESS DESIGN .1. FUNDAMENTALS AND ALGORITHMS [J].