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HPR-LP: An implementation of an HPR method for solving linear programming

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arxiv 2408.12179 v2 pith:ARU6J3C2 submitted 2024-08-22 math.OC

Kaihuang Chen , Defeng Sun , Yancheng Yuan , Guojun Zhang , Xinyuan Zhao This is my paper · ORCID
classification math.OC
keywords methodtextbfsolverbenchmarkcomplexitydatasetsdifferenthpr-lp
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abstract

In this paper, we introduce an HPR-LP solver, an implementation of a Halpern Peaceman-Rachford (HPR) method with semi-proximal terms for solving linear programming (LP). The HPR method enjoys the iteration complexity of $O(1/k)$ in terms of the Karush-Kuhn-Tucker residual and the objective error. Based on the complexity results, we design an adaptive strategy of restart and penalty parameter update to improve the efficiency and robustness of the HPR method. We conduct extensive numerical experiments on different LP benchmark datasets using NVIDIA A100-SXM4-80GB GPU in different stopping tolerances. Our solver's Julia version achieves a $\textbf{2.39x}$ to $\textbf{5.70x}$ speedup measured by SGM10 on benchmark datasets with presolve ($\textbf{2.03x}$ to $\textbf{4.06x}$ without presolve) over the award-winning solver PDLP with the tolerance of $10^{-8}$.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    Augmented Lagrangian subproblems inherit low-rankness, strict complementarity, and quadratic growth from a primal simple SDP, making Burer-Monteiro gradient descent converge linearly.

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    HPR-QP solves large-scale convex composite quadratic programs with a dual Halpern Peaceman-Rachford iteration on the restricted Wolfe dual, obtaining O(1/k) KKT residual and strong GPU benchmark results.

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    A restarted primal-dual method with a per-buyer bisection inner solve, run on GPUs, computes Fisher equilibria at ten-million-buyer scale and extends to Arrow-Debreu markets via fixed-point iteration.

  4. Peaceman-Rachford Splitting Method Converges Ergodically for Solving Convex Optimization Problems

    math.OC 2025-01 conditional novelty 6.0 of 10

    The ergodic (averaged) sequence of the semi-proximal Peaceman-Rachford splitting method converges to a solution of convex optimization problems with an O(1/k) complexity bound.

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    PyClustrPath is a new GPU-accelerated Python package for convex clustering that reports speedups of about 2.5x to 10x over existing CPU-based solvers on five benchmark datasets.

  6. An Overview of GPU-based First-Order Methods for Linear Programming and Extensions

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    A survey of GPU-based first-order LP solvers focusing on cuPDLP, its PDHG core, theory, benchmarks, and extensions to QP, SDP, and conic programming.

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