Stability of Nonhomogeneous Split Equality and Split Feasibility Problems with Possibly Nonconvex Constraint Sets

TL;DR

This paper investigates the stability of solutions to nonhomogeneous split equality and split feasibility problems with potentially nonconvex constraints, providing conditions for solution map stability using advanced variational analysis techniques.

Contribution

It introduces necessary and sufficient conditions for the Lipschitz-likeness of solution maps in nonconvex split problems, extending previous convex-focused stability results.

Findings

Established conditions for solution stability in nonconvex settings

Provided concrete examples illustrating the theoretical results

Extended classical stability analysis to more general nonconvex problems

Abstract

By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary and sufficient conditions for the Lipschitz-likeness of the solution maps of the problems are given and illustrated by concrete examples. The obtained results complement those given in [Huong VT, Xu HK, Yen ND. Stability analysis of split equality and split feasibility problems. arXiv:2410.16856.], where classical split equality problems and split feasibility problems have been considered.