Convergence,Scalarization and Continuity of Minimal Solutions in Set Optimization  

作　　者：Karuna C.S.Lalitha 

机构地区：[1]Department of Mathematics,University of Delhi,Delhi,Delhi,110007,India [2]Department of Mathematics,University of Delhi South Campus,New Delhi,Delhi,110021,India

出　　处：《Journal of the Operations Research Society of China》2024年第3期773-793,共21页中国运筹学会会刊（英文）

基　　金：supported by MATRICS scheme of Department of Science and Technology,India(No.MTR/2017/00016).

摘　　要：The paper deals with the study of two different aspects of stability in the given space as well as the image space,where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space.The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painlevé–Kuratowski set convergence of solution sets of the perturbed problems in the given space.The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems.The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.

关 键 词：Topological convergence Painlevé-Kuratowski convergence Upper semicontinuity Lower semicontinuity STABILITY SCALARIZATION 

分 类 号：O17[理学—数学]