Problem Structures in the Theory and Practice of Superiorization

TL;DR

This paper explores the fundamental mathematical concept underlying the superiorization methodology, aiming to generalize its application beyond specific problems by introducing the idea of problem structures.

Contribution

It introduces the concept of problem structures as an abstract mathematical framework to better understand and generalize superiorization methodology.

Findings

Identifies the mathematical essence of superiorization

Proposes a generalized framework using problem structures

Facilitates broader application of superiorization techniques

Abstract

The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently, superiorization is often presented using the terminology of such problems. A more general approach is provided here by discussing ideas related to superiorization in terms of an abstract mathematical concept, referred to as a problem structure.