{"ID":2872430,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.08256","arxiv_id":"2509.08256","title":"Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy","abstract":"Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important methods. This paper discusses different and novel kinds of advanced subspaces for such methods and presents a new algorithm with such subspaces, called MD-LAMBO. Theoretical analysis including the subspaces' properties, sufficient function value decrease, and global convergence is given for the new algorithm. The related model construction on the subspaces is given under derivative-free settings. In numerical results, performance profiles, and truncated Newton step errors of MD-LAMBO using different model-driven subspaces are provided, which show subspace-dependent numerical differences and advantages of our methods and subspaces.","short_abstract":"Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important methods. This paper discusses different and novel kinds of advanced subspaces for su...","url_abs":"https://arxiv.org/abs/2509.08256","url_pdf":"https://arxiv.org/pdf/2509.08256v1","authors":"[\"Yitong He\",\"Pengcheng Xie\"]","published":"2025-09-10T03:25:56Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[]","has_code":false}