Generalized Lagrangian Duality in Set-valued Vector Optimization via Abstract Subdifferential

作     者：Yan-fei CHAI San-yang LIU Si-qi WANG Yan-fei CHAI;San-yang LIU;Si-qi WANG

作者机构：Department of MathematicsXi'an Polytechnic UniversityXi'an 710048China School of Mathematics and StatisticsXidian UniversityXi'an 710071China College of Transportation EngineeringChang'an UniversityXi'an 710064China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2022年第38卷第2期

页      面：337-351页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Science Foundation of China(No.11401487) the Education Department of Shaanxi Province(No.17JK0330) the Fundamental Research Funds for the Central Universities(No.300102341101) State Key Laboratory of Rail Transit Engineering Informatization(No.211934210083) 

主　　题：Nonconvex set-valued vector optimization abstract subdifferential generalized augmented Lagrangian duality exact penalization sub-optimal path 

摘      要：In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract *** first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency,which used by the concepts of supremum and infimum of a *** then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object ***,we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization *** addition,we consider a generalized vector variational inequality as an application of abstract subdifferential.