On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization

作     者：Feng, Min Li, Shengjie Wang, Jie 

作者机构：Chongqing Jiaotong Univ Coll Math & Stat Chongqing 400074 Peoples R China Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：2022年第195卷第2期

页      面：480-503页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China Science and Technology Research Program of Chongqing Municipal Education Commission [KJQN202000740] Joint Training Base Construction Project for Graduate Students in Chongqing [JDLHPYJD2021016] 

主　　题：Nonsmooth multiobjective optimization Theorems of the alternative Properly efficient solutions Weak regularity conditions Strong Karush Kuhn-Tucker conditions 

摘      要：This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present a generalization of Tucker s alternative theorem for conic nonlinear systems, provided that a closedness condition holds. Some sufficient conditions for the validity of such a closedness condition are given. As applications, under the weak Abadie regularity condition, we then establish the primal and the strong Karush/Kuhn-Tucker (dual) necessary optimality conditions for an efficient solution to be locally properly efficient in Borwein s sense. The primal and the dual conditions are formulated as an equivalent pair by means of the Tucker-type alternative results. Finally we give an example to illustrate that Borwein s locally properly efficient solution cannot be reduced to the only efficient one in the main results.