均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

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.

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

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.