Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets

作     者：Chen, Jiawei Huang, La Li, Shengjie 

作者机构：Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China Chongqing Univ Coll Comp Sci Chongqing 400044 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：2018年第178卷第3期

页      面：794-823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：Natural Science Foundation of China [11401487, 11571055] Basic and Advanced Research Project of Chongqing [cstc2016jcyjA0239] China Postdoctoral Science Foundation [2015M582512] Fundamental Research Funds for the Central Universities [XDJK2018] 

主　　题：Constrained multiobjective optimization Image space analysis Improvement set Nonlinear separation Optimality condition 

摘      要：In this paper, we investigate the separations and optimality conditions for the optimal solution defined by the improvement set of a constrained multiobjective optimization problem. We introduce a vector-valued regular weak separation function and a scalar weak separation function via a nonlinear scalarization function defined in terms of an improvement set. The nonlinear separation between the image of the multiobjective optimization problem and an improvement set in the image space is established by the scalar weak separation function. Saddle point type optimality conditions for the optimal solution of the multiobjective optimization problem are established, respectively, by the nonlinear and linear separation methods. We also obtain the relationships between the optimal solution and approximate efficient solution of the multiobjective optimization problem. Finally, sufficient and necessary conditions for the (regular) linear separation between the approximate image of the multiobjective optimization problem and a convex cone are also presented.