An ${\cal O}(nL)$ Infeasible-Interior-Point Algorithm for Linear Programming

TL;DR

This paper introduces a new arc-search infeasible-interior-point algorithm for linear programming with a polynomial complexity bound of ${ m O}(nL)$, matching the best known theoretical performance.

Contribution

The paper presents a novel arc-search infeasible-interior-point algorithm with a proven polynomial complexity bound of ${ m O}(nL)$ for linear programming.

Findings

Algorithm is polynomial with complexity ${ m O}(nL)$

Complexity bound matches the best existing bounds

Proves polynomiality of the proposed method

Abstract

In this paper, we propose an arc-search infeasible-interior-point algorithm. We show that this algorithm is polynomial and the polynomial bound is ${\cal O}(nL)$ which is at least as good as the best existing bound for infeasible-interior-point algorithms for linear programming.