Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

TL;DR

This paper reviews the superiorization methodology, which aims to find feasible solutions that are better with respect to an objective function, bridging the gap between feasibility-seeking and constrained minimization.

Contribution

It clarifies the concepts of weak and strong superiorization and distinguishes their roles within the methodology.

Findings

Defines weak and strong superiorization approaches

Explains the relationship between feasibility and optimization

Provides insights into the methodology's applications

Abstract

We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full fledged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to an objective function value) to one returned by a feasibility-seeking only algorithm. We distinguish between two research directions in the superiorization methodology that nourish from the same general principle: Weak superiorization and strong superiorization and clarify their nature.