Isolated calmness and sharp minima via H\"older graphical derivatives

TL;DR

This paper introduces H"older graphical derivatives to characterize properties like isolated calmness and sharp minima, providing new insights into optimization stability and solution behavior.

Contribution

It develops a novel framework using H"older graphical derivatives to analyze strong subregularity, isolated calmness, and sharp minima in optimization problems.

Findings

Characterizes H"older isolated calmness in linear semi-infinite optimization

Identifies H"older sharp minimizers for penalty functions in constrained optimization

Provides theoretical tools for stability analysis in optimization

Abstract

The paper utilizes H\"older graphical derivatives for characterizing H\"older strong subregularity, isolated calmness and sharp minimum. As applications, we characterize H\"older isolated calmness in linear semi-infinite optimization and H\"older sharp minimizers of some penalty functions for constrained optimization.