一个标量泛函的研究及其在集值优化问题中的应用  

The Study of a Scalarizing Function with Application in Set-valued Optimization Problems

作　　者：张从军[1] 李赛 Cong Jun ZHANG;Sai LI(School of Applied Mathematics,Nanjing university of Finance and Economics, Nanjing 210023,P.R.China)

机构地区：[1]南京财经大学应用数学学院,南京210023

出　　处：《数学学报（中文版）》2019年第1期157-166,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11071109);江苏省自然科学基金项目(BK20171041);江苏省研究生科研创新项目(KYCX17_1204)

摘　　要：本文在K条件下,研究了所给标量泛函的连续性和拟凸性,并利用该标量泛函,将集值优化问题转化为均衡问题,进而研究了含约束的集值优化问题弱充分解的存在性和拟集值优化问题强逼近解映射的上半连续性与下半连续性.与最近的文献相比,我们的方法是新的,条件和结论也更具一般性.We investigate a scalarizing function’s continuity and convexity under K-conditions. Utilizing that function, we convert set-valued optimization problems into equilibrium problems,and then study existence of efficient solutions of set-valued optimization problems with constraints, the upper semicontinuity and lower semicontinuity of strongly approximate solution mappings to the parametric set-valued optimization problems. As compared with relevant literatures, our methods are new, our conclusions and conditions are more general.

关 键 词：标量泛函 集值优化问题 连续性 拟凸性 

分 类 号：O177.91[理学—数学]