{"ID":2847828,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.26061","arxiv_id":"2510.26061","title":"Data-driven Projection Generation for Efficiently Solving Heterogeneous Quadratic Programming Problems","abstract":"We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to generate projections tailored to each QP instance, enabling us to produce high-quality solutions even for previously unseen problems. The model is trained on heterogeneous QPs to minimize the expected objective value evaluated on the projected solutions. This is formulated as a bilevel optimization problem; the inner optimization solves the QP under a given projection using a QP solver, while the outer optimization updates the model parameters. We develop an efficient algorithm to solve this bilevel optimization problem, which computes parameter gradients without backpropagating through the solver. We provide a theoretical analysis of the generalization ability of solving QPs with projection matrices generated by neural networks. Experimental results demonstrate that our method produces high-quality feasible solutions with reduced computation time, outperforming existing methods.","short_abstract":"We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to generate projections tailored to each QP instance, enabling us to produce high-...","url_abs":"https://arxiv.org/abs/2510.26061","url_pdf":"https://arxiv.org/pdf/2510.26061v1","authors":"[\"Tomoharu Iwata\",\"Futoshi Futami\"]","published":"2025-10-30T01:32:21Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.AI\",\"cs.LG\",\"math.OC\"]","methods":"[\"Graph Neural Network\"]","has_code":false}