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arXiv · 2107.03570

Solving Linear Programs with Fast Online Learning Algorithms

Wenzhi Gao·Dongdong Ge·Chunlin Sun·Yinyu Ye
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Abstract

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a variable-duplication technique that copies each variable $K$ times and reduces the optimality gap and constraint violation by a factor of $\sqrt{K}$. Furthermore, we show how online algorithms can be effectively integrated into sifting, a column generation scheme for large-scale LPs. Numerical experiments demonstrate that our methods can serve as either an approximate direct solver, or an initialization subroutine for exact LP solving.

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Wenzhi Gao, Dongdong Ge, Chunlin Sun, Yinyu Ye. 2021-07-08. Solving Linear Programs with Fast Online Learning Algorithms. https://arxiv.org/abs/2107.03570

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