{"ID":2887581,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.01299","arxiv_id":"2508.01299","title":"A Frank-Wolfe-based primal heuristic for quadratic mixed-integer optimization","abstract":"We propose a primal heuristic for quadratic mixed-integer problems. Our method extends the Boscia framework -- originally a mixed-integer convex solver leveraging a Frank-Wolfe-based branch-and-bound approach -- to address nonconvex quadratic objective and constraints. We reformulate nonlinear constraints, introduce preprocessing steps, and a suite of heuristics including rounding strategies, gradient-guided selection, and large neighborhood search techniques that exploit integer-feasible vertices generated during the Frank-Wolfe iterations. Computational results demonstrate the effectiveness of our method in solving challenging MIQCQPs, achieving improvements on QPLIB instances within minutes and winning first place in the Land-Doig MIP Computational Competition 2025.","short_abstract":"We propose a primal heuristic for quadratic mixed-integer problems. Our method extends the Boscia framework -- originally a mixed-integer convex solver leveraging a Frank-Wolfe-based branch-and-bound approach -- to address nonconvex quadratic objective and constraints. We reformulate nonlinear constraints, introduce pr...","url_abs":"https://arxiv.org/abs/2508.01299","url_pdf":"https://arxiv.org/pdf/2508.01299v2","authors":"[\"Gioni Mexi\",\"Deborah Hendrych\",\"Sébastien Designolle\",\"Mathieu Besançon\",\"Sebastian Pokutta\"]","published":"2025-08-02T10:17:32Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}