HOLDER CONTINUITY RESULTS FOR PARAMETRIC SET OPTIMIZATION PROBLEMS VIA IMPROVEMENT SETS

摘要

In this paper, we consider a class of parametric set optimization problems, where both objective functions and constraint functions are perturbed by different parameters. Firstly, upper and lower set orderings with respect to improvement sets are introduced and used to define solution mappings. Then, some assumptions including strong domination properties are proposed to study the Holder continuity of solution mappings and corresponding optimal value mappings. Our results generalize the upper Holder continuity of efficient solution mappings for parametric vector optimization problems.