{
  "abstract": "Piecewise-linear (PWL) optimization problems arise in many mixed-integer programming (MIP) optimization applications, including portfolio optimization, workforce scheduling, and resource allocation. But solving them to global optimality remains computationally expensive because branch-and-bound repeatedly solves LP relaxation subproblems. Existing solvers are largely CPU-centric, leaving the scalability of modern GPUs underutilized. Few prior GPU-accelerated branch-and-bound either targets neural network which is not suitable for general PWL optimization, or accelerates only auxiliary subroutines such as strong branching heuristics within CPU-centric MIP solvers. To bridge this gap, we propose B$^3$-PWL, a GPU-centric batched branch-and-bound framework for piecewise-linear optimization with Special Ordered Set of type 2 (SOS2) constraints. Our method solves batches of LP relaxation subproblems concurrently on the GPU using a first-order primal-dual solver, enabled by a specialized batched block-tiled sparse matrix kernel. To complement bound computation, we further introduce a unified feasibility search module that combines an SOS2 repair primal heuristic with a batched feasibility pump to rapidly obtain feasible incumbents and improve pruning efficiency. On a benchmark of 43 PWL-MIP instances, B$^3$-PWL achieves a 9.25x geometric-mean speedup over NVIDIA cuOpt while reaching high-quality feasible incumbents on every tested instance. On a public valve-point unit-commitment benchmark, it further outperforms NVIDIA cuOpt and the open-source CPU solvers SCIP and HiGHS, demonstrating the potential of first-order LP methods as the central engine of GPU-accelerated branch-and-bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28988",
  "author_total": 5,
  "authors": [
    {
      "name": "Yilin Guan"
    },
    {
      "name": "Shuqing Luo"
    },
    {
      "name": "Pingzhi Li"
    },
    {
      "name": "Tianlong Chen"
    },
    {
      "name": "Kaidi Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8r9btehs6wf1t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28988",
  "fulltext_url": null,
  "id": "8r9btehs6wf1t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28988",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DC"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7204898559",
  "pdf_url": "https://arxiv.org/pdf/2608.28988",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8r9btehs6wf1t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28988",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28988"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "B$^3$-PWL: GPU-Batched Branch-and-Bound for Piecewise-Linear Optimization with SOS2 Constraints",
  "title_text": "B^3-PWL: GPU-Batched Branch-and-Bound for Piecewise-Linear Optimization with SOS2 Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8r9btehs6wf1t",
  "venue": "arXiv",
  "versions": []
}