Continuity of maximal value functionals in normed spaces

被引：0
|
作者：
Jahn J. [1 ]
机构：
[1] Department Mathematik, Universität Erlangen-Nürnberg, Cauerstr. 11, Erlangen
来源：
Applied Set-Valued Analysis and Optimization | 2021年 / 3卷 / 03期
关键词：
Maximal value functional; Necessary optimality condition; Set optimization;
D O I：
10.23952/ASVAO.3.2021.3.06
中图分类号：
O144 [集合论]; O157 [组合数学（组合学）];
学科分类号：
070104 ;
摘要：
This paper examines special maximal value functionals, which are extended support functionals where the objective is linear but the constraint set is nonconvex. In finite-dimensional spaces, it is well-known that these maximal value functionals are continuous. It is shown in the present paper that this result can also be proven in normed spaces without convexity assumptions. As an application, necessary optimality conditions in set optimization are derived. © 2021 Applied Set-Valued Analysis and Optimization.
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页码：317 / 323
页数：6
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