Approximate Weak Minimal Solutions of Set-Valued Optimization Problems  

作　　者：S.Khoshkhabar-amiranloo 

机构地区：[1]School of Mathematics,Institute for Research in Fundamental Sciences,Tehran,Iran

出　　处：《Journal of the Operations Research Society of China》2023年第3期673-692,共20页中国运筹学会会刊（英文）

基　　金：Institute for Research in Fundamental Sciences(No.96580048).

摘　　要：This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.

关 键 词：Set-valued optimization Approximate weak minimal solutions Existence theorems Optimality conditions Scalarization functions 

分 类 号：O17[理学—数学]