集值优化问题近似解的最优条件

Optimality conditions of approximate efficient solutions for set-valued optimization problems

在实赋范线性空间中建立一类集值优化问题近似解的最优条件和对偶定理.在锥-逼近多值函数概念的基础上,借助锥-次不变凸性,研究最优条件和对偶定理.运用分析的方法,在广义凸性假设条件下,得到Henig近似解极小点和Global近似解极小点的最优条件,及Mond-Weir和Wolfe模型下的弱对偶定理、强对偶定理和逆对偶定理.研究成果可丰富和发展集值优化理论算法及其应用.

This paper established optimality conditions and duality theorems of approximate solutions to a kind of set-valued optimization problems in real normed vector space.Based upon the concept of cone-approximating multifunction,the optimality conditions and duality theo-rems by means of cone-subinvexity were studied.Using the analytic method,under the generalized convexity assumption,the paper obtained the optimality conditions for the Henig approximate efficient solution minimizers and Global approximate efficient solution minimizers to the set-valued optimization problems,and gained the weak duality theorem,strong duality theorem and inverse duality theorem in sense of Mond-Weir and Wolfe models.These results enriched and developed the algorithm and application of set-valued optimization theory.