Log-domain interior-point methods for convex quadratic programming

TL;DR

This paper introduces and analyzes log-domain interior-point methods for convex quadratic programming, proving their polynomial convergence and demonstrating superior practical performance over classical barrier methods.

Contribution

It is the first to study log-domain interior-point methods for quadratic programming and establishes their theoretical convergence and practical advantages.

Findings

Proved polynomial-time convergence of log-domain interior-point methods.

Showed that these methods are approximated by classical barrier methods.

Provided computational experiments demonstrating superior performance.

Abstract

Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these conditions in the log-domain is a natural variation on this approach that to our knowledge is previously unstudied. In this paper, we analyze log-domain interior-point methods and prove their polynomial-time convergence. We also prove that they are approximated by classical barrier methods in a precise sense and provide simple computational experiments illustrating their superior performance.