Non-Convex Split Feasibility Problems: Models, Algorithms and Theory

TL;DR

This paper introduces various iterative algorithms for solving non-convex split feasibility problems, providing theoretical convergence guarantees and exploring different models suited for diverse problem settings.

Contribution

It presents a comprehensive catalog of models and algorithms, including new methods, with proven global convergence in the non-convex context.

Findings

All studied methods have global convergence guarantees.

The paper compares different models for various problem settings.

Some algorithms are newly proposed in this work.

Abstract

In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different settings of the problem. For each model, we study relevant iterative algorithms, some of which are well-known in this area and some are new. All the studied methods, including the well-known CQ Algorithm, are proven to have global convergence guarantees in the non-convex setting under mild conditions on the problem's data.