Interior-Point Algorithms for Monotone Linear Complementarity Problem Based on Different Predictor Directions
Optimization and Control
2025-07-31 v1
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.
Cite
@article{arxiv.2507.22185,
title = {Interior-Point Algorithms for Monotone Linear Complementarity Problem Based on Different Predictor Directions},
author = {Marianna E. -Nagy and Tibor Illés and Yurii Nesterov and Petra Renáta Rigó},
journal= {arXiv preprint arXiv:2507.22185},
year = {2025}
}