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

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

机构地区：[1]Department of Mathematics,Xi'an Polytechnic University,Xi'an 710048,China [2]School of Mathematics and Statistics,Xidian University,Xi'an 710071,China [3]College of Transportation Engineering,Chang'an University,Xi'an 710064,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第2期337-351,共15页应用数学学报（英文版）

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)。

摘　　要：In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential.We 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 set.We 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 map.Finally,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 problem.In addition,we consider a generalized vector variational inequality as an application of abstract subdifferential.

关 键 词：Nonconvex set-valued vector optimization abstract subdifferential generalized augmented Lagrangian duality exact penalization sub-optimal path 

分 类 号：O174[理学—数学]