Metric Regularity of the Sum of Multifunctions and Applications

TL;DR

This paper investigates the metric regularity of the sum of multifunctions using error bounds and epigraphical multifunctions, extending recent results in variational analysis.

Contribution

It introduces a novel approach based on the metric regularity of epigraphical multifunctions to analyze the sum of multifunctions, generalizing previous findings.

Findings

Established new conditions for metric regularity of multifunction sums

Extended existing results by Durea and Strugariu

Applied the theory to variational systems

Abstract

In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical multifunctions. Our results subsume some recent results by Durea and Strugariu.