On Hölder calmness of minimizing sets. (3rd April 2022)

• Record Type: Journal Article
• Authors: Klatte, Diethard; Kummer, Bernd
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 1055
• Page End: 1072
• Publication Date: 2022-04-03
• Subjects: Perturbed optimization problems -- minimizing sets -- stability conditions -- Hölder calmness -- upper Hölder continuity; 49J53 -- 90C31 -- 90C25 -- 90C34; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1914038
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We present conditions for Hölder calmness and upper Hölder continuity of optimal solution sets to perturbed optimization problems in finite dimensions. Studies on Hölder type stability were a popular subject in variational analysis already in the 1980s and 1990s, and have become a revived interest in the last decade. In this paper, we focus on conditions for Hölder calmness of the argmin mapping in the case of non-isolated minima. We recall known ideas and results in this context for general as well as special parametric programs, refine them and discuss particular settings, including nonlinear programs and convex semi-infinite optimization problems.