Interior-Point Algorithms for Monotone Linear Complementarity Problem Based on Different Predictor Directions

TL;DR

This paper presents two novel interior-point algorithms for monotone linear complementarity problems, achieving optimal worst-case complexity and local quadratic convergence, with promising numerical performance.

Contribution

It introduces two new interior-point methods based on predictor directions for monotone LCPs, with proven complexity bounds and convergence properties.

Findings

The first algorithm has the best known worst-case complexity.

The auto-correcting version converges quadratically locally.

Numerical experiments show competitive performance.

Abstract

In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for linear optimization problems. We prove that this method has the best known worst-case complexity bound. We extend onto LCP its auto-correcting version, and prove its local quadratic convergence under a non-degeneracy assumption. In our numerical experiments, we compare the new algorithms with a general method, recently developed for weighted monotone linear complementarity problems.