Directional H\"older Metric Regularity

TL;DR

This paper explores the properties of directional H"older and Lipschitz metric regularity of multifunctions, providing new characterizations and demonstrating their stability under perturbations, with applications to optimization problem sensitivity analysis.

Contribution

It introduces novel characterizations of directional H"older/Lipschitz metric regularity based on slope and coderivative concepts, and shows their stability under perturbations.

Findings

Directional H"older/Lipschitz metric regularity is stable under suitable perturbations.

New characterizations of regularity using slope and coderivative.

Applications to stability and sensitivity analysis in optimization.

Abstract

This paper sheds new light on regularity of multifunctions through various characterizations of directional H\"older /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional H\"older /Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional H\"older /Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.