Batched First-Order Methods for Parallel LP Solving in MIP

Fuente: arXiv
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Hauptverfasser: Blin, Nicolas, Gualandi, Stefano, Maes, Christopher, Lodi, Andrea, Stellato, Bartolomeo
Format: Preprint
Veröffentlicht: 2026
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author Blin, Nicolas
Gualandi, Stefano
Maes, Christopher
Lodi, Andrea
Stellato, Bartolomeo
author_facet Blin, Nicolas
Gualandi, Stefano
Maes, Christopher
Lodi, Andrea
Stellato, Bartolomeo
contents We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise in mixed-integer programming techniques such as strong branching and bound tightening. By leveraging matrix-matrix operations instead of repeated matrix-vector operations, we obtain significant computational advantages on GPU architectures. We demonstrate the effectiveness of our approach on various case studies and identify the problem sizes where first-order methods outperform traditional simplex-based solvers depending on the computational environment one can use. This is a significant step for the design and development of integer programming algorithms tightly exploiting GPU capabilities where we argue that some specific operations should be allocated to GPUs and performed in full instead of using light-weight heuristic approaches on CPUs.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21990
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Batched First-Order Methods for Parallel LP Solving in MIP
Blin, Nicolas
Gualandi, Stefano
Maes, Christopher
Lodi, Andrea
Stellato, Bartolomeo
Optimization and Control
Machine Learning
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise in mixed-integer programming techniques such as strong branching and bound tightening. By leveraging matrix-matrix operations instead of repeated matrix-vector operations, we obtain significant computational advantages on GPU architectures. We demonstrate the effectiveness of our approach on various case studies and identify the problem sizes where first-order methods outperform traditional simplex-based solvers depending on the computational environment one can use. This is a significant step for the design and development of integer programming algorithms tightly exploiting GPU capabilities where we argue that some specific operations should be allocated to GPUs and performed in full instead of using light-weight heuristic approaches on CPUs.
title Batched First-Order Methods for Parallel LP Solving in MIP
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2601.21990