{"ID":2889376,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.22185","arxiv_id":"2507.22185","title":"Interior-Point Algorithms for Monotone Linear Complementarity Problem Based on Different Predictor Directions","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.","short_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...","url_abs":"https://arxiv.org/abs/2507.22185","url_pdf":"https://arxiv.org/pdf/2507.22185v1","authors":"[\"Marianna E. -Nagy\",\"Tibor Illés\",\"Yurii Nesterov\",\"Petra Renáta Rigó\"]","published":"2025-07-29T19:29:44Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}