均衡约束数学规划问题的Mond-Weir型对偶理论

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均衡约束数学规划问题的Mond-Weir型对偶理论

高雷阜¹,闫婷婷²

1. 辽宁工程技术大学理学院
2. 辽宁工程技术大学

收稿日期:2017-06-12 修回日期:2017-07-23 发布日期:2019-03-05
通讯作者: 高雷阜

MOND-WEIR TYPE DUALITY THEORY FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS

Received:2017-06-12 Revised:2017-07-23 Published:2019-03-05

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, 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, based on the dual form of standard nonlinear programming proposed by Mond and Weir, using the S-stability, we establish the Mond-Weir type duality of equilibrium constrained optimization problem, which 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 theorem 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), Mond-Weir type duality, stability point

高雷阜闫婷婷. 均衡约束数学规划问题的Mond-Weir型对偶理论[J]. 运筹学学报.

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均衡约束数学规划问题的Mond-Weir型对偶理论

MOND-WEIR TYPE DUALITY THEORY FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS

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