BCQ and Strong BCQ for Nonconvex Generalized Equations with Applications to Metric Subregularity

TL;DR

This paper explores constraint qualifications for nonconvex generalized equations, establishing their characterizations and applying them to analyze metric subregularity, providing conditions to ensure this property in nonconvex settings.

Contribution

It extends BCQ and strong BCQ concepts from convex to nonconvex generalized equations, offering new characterizations and applications to metric subregularity analysis.

Findings

Characterizations of BCQ and strong BCQ for nonconvex generalized equations

Necessary and sufficient conditions for metric subregularity

Application of constraint qualifications to ensure subregularity

Abstract

In this paper, based on basic constraint qualification (BCQ) and strong BCQ for convex generalized equation, we are inspired to further discuss constraint qualifications of BCQ and strong BCQ for nonconvex generalized equation and then establish their various characterizations. As applications, we use these constraint qualifications to study metric subregularity of nonconvex generalized equation and provide necessary and/or sufficient conditions in terms of constraint qualifications considered herein to ensure nonconvex generalized equation having metric subregularity.