非凸集值优化问题严有效解的强对偶定理

摘要

This paper is diverted to the study of two strong dual problems of a primal nonconvex set-valued optimization in the sense of strict efficiency. By using the principles of Lagrange duality and Mond-Weir duality, for each dual problem, a strong duality theorem with strict efficiency is established. The conclusions can be formulated as follows: starting from a strictly efficient solution of the primal problem, it can be constructed a strictly efficient solution of the dual problem such that the corresponding objective values of both problems are equal. The results generalize the strong dual theorems in which the set-valued maps are assumed to be cone-convex.%本文研究了非凸集值向量优化的严有效解在两种对偶模型的强对偶问题.利用Lagrange对偶和Mond-Weir对偶原理,获得了如下结果:原集值优化问题的严有效解,在一些条件下是对偶问题的强有效解,并且原问题和对偶问题的目标函数值相等;推广了集值优化对偶理论在锥-凸假设下的相应结果.