{"ID":2856030,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.10891","arxiv_id":"2510.10891","title":"Successive Fixing for Large-Scale SCUC Using First-Order Methods","abstract":"Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within branch-and-cut. Conventional simplex and barrier methods become computationally prohibitive at this scale due to their reliance on expensive matrix factorizations. While matrix-free first-order methods present a promising alternative, their tendency to converge to non-vertex solutions renders them incompatible with standard branch-and-cut procedures. To bridge this gap, we propose a successive fixing framework that leverages a customized GPU-accelerated first-order LP solver to guide a logic-driven variable-fixing strategy. Each iteration produces a reduced Mixed-Integer Linear Programming (MILP) problem, which is subsequently tightened via presolving. This iterative cycle of relaxation, fixing, and presolving progressively reduces problem complexity, producing a highly tractable final MILP model. When evaluated on public benchmarks exceeding 13,000 buses, our approach achieves a tenfold speedup over state-of-the-art methods without compromising solution quality.","short_abstract":"Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within branch-and-cut. Conventional simplex and barrier methods become computationally prohibitive at...","url_abs":"https://arxiv.org/abs/2510.10891","url_pdf":"https://arxiv.org/pdf/2510.10891v1","authors":"[\"Jinxin Xiong\",\"Yanting Huang\",\"Yingxiao Wang\",\"Linxin Yang\",\"Jianghua Wu\",\"Shunbo Lei\",\"Akang Wang\"]","published":"2025-10-13T01:39:08Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}