A polynomial time infeasible interior-point arc-search algorithm for convex optimization

TL;DR

This paper introduces a new polynomial-time infeasible interior-point algorithm for convex optimization that uses arc-search techniques to improve efficiency and convergence, with proven theoretical guarantees and promising preliminary results.

Contribution

It presents a novel arc-search based interior-point method that adaptively chooses parameters, with proven polynomial convergence and efficiency improvements over existing methods.

Findings

Algorithm is proven to converge polynomially.

Preliminary tests show the method is efficient and effective.

Analytic formulas enhance the efficiency of arc-search.

Abstract

This paper proposes an infeasible interior-point algorithm for the convex optimization problem using arc-search techniques. The proposed algorithm simultaneously selects the centering parameter and the step size, aiming at optimizing the performance in every iteration. Analytic formulas for the arc-search are provided to make the arc-search method very efficient. The convergence of the algorithm is proved and a polynomial bound of the algorithm is established. The preliminary numerical test results indicate that the algorithm is efficient and effective.