On Hölder Calmness of Minimizing Sets

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 1980ies and 1990ies, 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.


Preprint (revised version), Institut für Betriebswirtschaftslehre, Universität Zürich, March 2021. The final version of this paper is accepted for publication in "Optimization".



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