H\"older Error Bounds and H\"older Calmness with Applications to Convex Semi-Infinite Optimization

TL;DR

This paper investigates H"older error bounds and calmness in convex semi-infinite optimization using variational analysis, providing new conditions, estimates, and characterizations relevant for optimization stability analysis.

Contribution

It offers new subdifferential conditions for H"older error bounds and characterizes H"older calmness of the argmin mapping in convex semi-infinite optimization.

Findings

Derived necessary and sufficient subdifferential conditions for H"older error bounds.

Provided estimates for the H"older calmness modulus in convex semi-infinite optimization.

Characterized the H"older calmness of the argmin mapping via level set and supremum functions.

Abstract

Using techniques of variational analysis, necessary and sufficient subdifferential conditions for H\"older error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the H\"older calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the H\"older calmness modulus of the argmin mapping in the framework of linear programming.