Continuity of maximal value functionals in normed spaces - Jahn, Johannes (Applied Set-Valued Analysis and Optimization, 2021)
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.
CRIS-Team Scopus Importer:2021-11-19
Keywords: Maximal value functional; Necessary optimality condition; Set optimization