On the Effectiveness of Projection Methods for Convex Feasibility Problems with Linear Inequality Constraints

TL;DR

This paper evaluates projection methods for solving large-scale linear inequality systems, demonstrating their computational advantages and practical success through extensive experiments and literature review.

Contribution

It provides empirical evidence of the efficiency of projection methods for large convex feasibility problems with linear inequalities, highlighting their practical applicability.

Findings

Projection methods outperform some alternatives in computational efficiency

Effective for problems with tens of thousands of unknowns and constraints

Proven successful in real-world applications and large-scale problems

Abstract

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of unknowns satisfying up to hundreds of thousands of constraints) and by a discussion of the demonstrated efficacy of projection methods in numerous scientific publications and commercial patents (dealing with problems that can have over a billion unknowns and a similar number of constraints).