On a robust approach to "split" feasibility problems: solvability and global error bound conditions

TL;DR

This paper develops a robust convex feasibility framework for split problems, establishing conditions for solution existence and error bounds using variational analysis, with particular focus on polyhedral cases.

Contribution

It introduces a reformulation of robust split feasibility problems as set-valued inclusions, providing new solvability and stability conditions.

Findings

Established sufficient conditions for solution existence.

Derived error bounds based on problem data.

Analyzed robust polyhedral split feasibility problems.

Abstract

In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds are investigated. This is done by reformulating the robust counterpart of a split feasibility problem as a set-valued inclusion, a problem for which one can take profit from the solvability and stability theory that has been recently developed. As a result, a sufficient condition for solution existence and error bounds is established in terms of problem data and discussed through several examples. A specific focus is devoted to error bound conditions in the case of the robust counterpart of polyhedral split feasibility problems.