Generic stability of the solution mapping for set-valued optimization problems

Journal of inequalities and applications

Xian-Jun Long¹ 

关键词: generic stability;    set-valued optimization problem;    weakly efficient solution;    essential;    semicontinuity;    49J53;    90C29;    90C31;   

DOI  :  10.1186/s13660-015-0875-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider the generic stability of the weakly efficient solution mapping for set-valued optimization problems. Firstly, we obtain the upper semicontinuity of the weakly efficient solution mapping for set-valued optimization problems. Secondly, we show that, in the sense of Baire category, most set-valued optimization problems are stable. Finally, we give sufficient conditions ensuring the existence of essential. Our results extend and improve the corresponding results of Song et al. (J. Optim. Theory Appl. 156:591-599, 2013).

【 授权许可】

CC BY