均衡约束数学规划的约束规格和最优性条件综述

运筹学学报 ›› 2013, Vol. 17 ›› Issue (3): 73-85.

均衡约束数学规划的约束规格和最优性条件综述

黎健玲¹, 谢琴¹, 简金宝^2,*

1. 广西大学数学与信息科学学院，南宁 530004 2. 玉林师范学院数学与信息科学学院，广西玉林 537000

出版日期:2013-09-15 发布日期:2013-09-15
通讯作者: 简金宝 E-mail:jianjb@gxu.edu.cn
基金资助:
国家自然科学基金(No. 11271086)，广西自然科学基金(No. 2012GXNSFAA053007), 广西高等学校重点资助科研项目(No. 201102ZD002), 广西硕士研究生科研创新项目(No. YCSZ2013011)

Review on constraint qualifications and optimality conditions for mathematical programs with equilibrium constraints

LI Jianling¹, XIE Qin¹, JIAN Jinbao^2,*

1. ；College of Mathematics and Information Science, Guangxi University, Nanning 530004, China 2. Department of Mathematics and Computer Science, Yulin Normal University, Yulin 537000, Guangxi, China

Online:2013-09-15 Published:2013-09-15

摘要/Abstract

摘要： 约束规格在约束优化问题的最优性条件中起着重要的作用，介绍了近几年国际上关于均衡约束数学规划(简记为MPEC)的约束规格以及最优性条件的研究成果, 包括以下主要内容: (1) MPEC常用的约束规格(如线性无关约束规格 (MPEC-LICQ)、Mangasarian-Fromovitz约束规格 (MPEC-MFCQ)等)和新的约束规格(如恒秩约束规格、常数正线性相关约束规格等), 以及它们之间的关系; (2) MPEC常用的稳定点; (3) MPEC的最优性条件. 最后还对MPEC的约束规格和最优性条件的研究前景进行了探讨.

关键词: 均衡约束, 数学规划, 约束规格, 稳定点, 最优性条件

Abstract: This is a survey on constraint qualifications and optimality conditions for mathematical programs with equilibrium constraints (MPEC for short). Some important international research results on constraint qualifications and the corresponding optimality conditions for MPEC are introduced. The context included are as follows: (1) Some constraint qualifications in common use for MPEC (e.g., MPEC-LICQ, MPEC-MFCQ) and some latest developed constraint qualifications (e.g., constant rank constraint qualifications), and their relationships; (2) Various stationary points for MPEC; (3) Optimality conditions for MPEC. Finally, we discuss some future research perspectives of constraint qualifications and optimality conditions for MPEC.

Key words: equilibrium constraint, mathematical programs, constraint qualification, stationary points, optimality conditions

中图分类号:

O221

黎健玲, 谢琴, 简金宝. 均衡约束数学规划的约束规格和最优性条件综述[J]. 运筹学学报, 2013, 17(3): 73-85.

LI Jianling, XIE Qin, JIAN Jinbao. Review on constraint qualifications and optimality conditions for mathematical programs with equilibrium constraints[J]. Operations Research Transactions, 2013, 17(3): 73-85.

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