Can Linear Superiorization Be Useful for Linear Optimization Problems?

TL;DR

This paper explores the effectiveness of linear superiorization, a method that guides feasibility-seeking algorithms towards lower target function values, and finds it competitive with traditional linear programming methods like the Simplex algorithm.

Contribution

The study provides experimental evidence that linear superiorization can produce feasible points with lower target function values and performs very well compared to the Simplex method.

Findings

Linear superiorization often yields lower target function values than unperturbed feasibility algorithms.

It performs very well in comparison with the Simplex method.

Experimental results support its potential as an alternative approach.

Abstract

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: "yes" and "very well", respectively.