A polynomial projection-type algorithm for linear programming

TL;DR

This paper introduces a polynomial-time algorithm for linear programming feasibility that improves upon previous methods by replacing recursion with an efficient iterative approach, enhancing computational efficiency.

Contribution

It presents a new polynomial projection-type algorithm for linear programming feasibility, simplifying and improving upon Chubanov's divide-and-conquer method.

Findings

Algorithm runs in O([n^5/ extlog n]L) time

Provides a more efficient iterative method over recursive approaches

Advances polynomial-time solutions for linear programming feasibility

Abstract

We propose a simple O([n^5/\log n]L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chubanov's "Divide-and-Conquer" algorithm [4], where the recursion is replaced by a simple and more efficient iterative method. A similar approach was used in a more recent paper of Chubanov [6].