{"ID":2847398,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27117","arxiv_id":"2510.27117","title":"GFORS: GPU-Accelerated First-Order Method with Randomized Sampling for Binary Integer Programs","abstract":"We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that generates batched binary candidates. Both components are designed to run end-to-end on GPUs with minimal CPU-GPU synchronization. The framework establishes near-stationary-point guarantees for the first-order routine and probabilistic bounds on the feasibility and quality of sampled solutions, while not providing global optimality certificates. To improve sampling effectiveness, we introduce techniques such as total-unimodular reformulation, customized sampling design, and monotone relaxation. On classic benchmarks (set cover, knapsack, max cut, 3D assignment, facility location), baseline state-of-the-art exact solvers remain stronger on small-medium instances, while GFORS attains high-quality incumbents within seconds; on large instances, GFORS yields substantially shorter runtimes, with solution quality often comparable to -- or better than -- the baseline under the same time limit. These results suggest that GFORS can complement exact solvers by delivering scalable, GPU-native search when problem size and response time are the primary constraints.","short_abstract":"We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that generates batched binary candidates. Both components are designed to run end-to-end...","url_abs":"https://arxiv.org/abs/2510.27117","url_pdf":"https://arxiv.org/pdf/2510.27117v1","authors":"[\"Ningji Wei\",\"Jiaming Liang\"]","published":"2025-10-31T02:37:47Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}