Enhanced PDHG for Linear Programming with Online Preconditioning
Haihao Lu, Wanyu Zhang
TL;DR
This paper introduces an online preconditioning method for the PDHG algorithm in linear programming, which adaptively updates preconditioners to improve convergence speed and computational efficiency.
Contribution
It proposes a novel online preconditioning technique with algorithmic enhancements, implemented on GPU-based solvers, and validated through benchmarking on standard datasets.
Findings
Reduces iteration counts in LP solving
Decreases overall solving time
Effective on standard LP datasets
Abstract
We present an online preconditioning technique for the primal-dual hybrid gradient (PDHG) algorithm for linear programming (LP). The method adaptively updates primal and dual preconditioners using an online optimization framework. To improve its practical performance, we introduce several algorithmic enhancements, including using normalized online loss functions and updating preconditioners infrequently. We implement the technique on top of vanilla PDHG and the GPU-based LP solver cuPDLP.jl, and benchmark its performance on standard LP datasets. Our numerical experiments demonstrate that online preconditioning effectively reduces both iteration counts and overall solving time.
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