On Metric Subregularity for Convex Constraint Systems by Primal Equivalent Conditions

TL;DR

This paper investigates metric subregularity in convex constraint systems, establishing primal conditions via geometric tools and linking them to strong constraint qualifications, enhancing understanding of stability conditions.

Contribution

It provides new primal equivalent conditions for metric subregularity using contingent cones and graphical derivatives, connecting them to strong basic constraint qualifications.

Findings

Primal conditions characterize metric subregularity.

Conditions relate to contingent cones and graphical derivatives.

Link established with strong basic constraint qualification.

Abstract

In this paper, we mainly study metric subregularity for a convex constraint system defined by a convex set-valued mapping and a convex constraint subset. The main work is to provide several primal equivalent conditions for metric subregularity by contingent cone and graphical derivative. Further it is proved that these primal equivalent conditions can characterize strong basic constraint qualification of convex constraint system given by Zheng and Ng [SIAM J. Optim., 18(2007), pp. 437-460].