均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

doi:10.15960/j.cnki.issn.1007-6093.2019.02.009

运筹学学报 ›› 2019, Vol. 23 ›› Issue (2): 95-103.doi: 10.15960/j.cnki.issn.1007-6093.2019.02.009

均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

高雷阜^*, 闫婷婷

辽宁工程技术大学优化与决策研究所, 辽宁阜新 123000

收稿日期:2017-06-12 出版日期:2019-06-15 发布日期:2019-06-15
通讯作者: 高雷阜 E-mail:gaoleifu@163.com
基金资助:
高等学校博士学科点专项科研基金（No.20132121110009），辽宁省教育厅基金（No.L2015208）

A class of generalized mond-weir type duality theory for mathematical programs with equilibrium constraints

GAO Leifu^*, YAN Tingting

Institute of Optimization and Decision, Liaoning Technical University, Fuxin 123000, Liaoning, China

Received:2017-06-12 Online:2019-06-15 Published:2019-06-15

摘要/Abstract

摘要： 针对均衡约束数学规划模型难以满足约束规范及难于求解的问题，基于Mond和Weir提出的标准非线性规划的对偶形式，利用其S稳定性，建立了均衡约束数学规划问题的一类广义Mond-Weir型对偶，从而为求解均衡约束优化问题提供了一种新的方法.在Hanson-Mond广义凸性条件下，利用次线性函数，分别提出了弱对偶性、强对偶性和严格逆对偶性定理，并给出了相应证明.该对偶化方法的推广为研究均衡约束数学规划问题的解提供了理论依据.

关键词: 均衡约束数学规划, 广义Mond-Weir型对偶, 稳定点

Abstract: In this paper, considering the mathematical programs with equilibrium constraints is difficult to meet the constrained qualification and difficult to solve, we establish a class of generalized Mond-Weir type duality of equilibrium constrained optimization problem. Using the S-stability, we propose the duality theory, which is based on the dual form of standard nonlinear programming proposed by Mond and Weir. The theory provides a new method for solving the problem of equilibrium constraint optimization. Under the condition of Hanson-Mond generalized convexity, the weak duality, strong duality and strict inverse duality theorems are proposed by using the sublinear function, and the corresponding proofs are given. The generalization of the dual method provides a theoretical basis for studying the solution of the mathematical programs with equilibrium constraints.

Key words: mathematical programs with equilibrium constraints (MPEC), generalized Mond-Weir type duality, stability point

中图分类号:

O224

高雷阜, 闫婷婷. 均衡约束数学规划问题的一类广义Mond-Weir型对偶理论[J]. 运筹学学报, 2019, 23(2): 95-103.

GAO Leifu, YAN Tingting. A class of generalized mond-weir type duality theory for mathematical programs with equilibrium constraints[J]. Operations Research Transactions, 2019, 23(2): 95-103.

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均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

A class of generalized mond-weir type duality theory for mathematical programs with equilibrium constraints

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