A new search direction for full-Newton step infeasible interior-point method in linear optimization

TL;DR

This paper introduces a novel infeasible interior-point method with a full-Newton step for linear optimization, utilizing an algebraic transformation to improve convergence analysis and polynomial-time guarantees.

Contribution

The paper proposes a new search direction based on an algebraic transformation of the centering equation, ensuring polynomial-time convergence for the infeasible interior-point method.

Findings

Method finds an ε-optimal solution in polynomial time.

The algebraic transformation simplifies the analysis of the central path.

The approach extends the class of feasible interior-point methods.

Abstract

In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central path. We prove that the method finds an $\varepsilon$-optimal solution of the underlying problem in polynomial time.