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arXiv · 2111.05530

Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming

Haihao Lu·Jinwen Yang
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Abstract

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the proposed stochastic method exhibits a linear convergence rate for solving sharp instances with a high probability. In addition, we propose an efficient coordinate-based stochastic oracle for unconstrained bilinear problems, which has $\mathcal O(1)$ per iteration cost and improves the complexity of the existing deterministic and stochastic algorithms. Finally, we show that the obtained linear convergence rate is nearly optimal (upto $\log$ terms) for a wide class of stochastic primal dual methods.

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Haihao Lu, Jinwen Yang. 2021-11-10. Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming. https://arxiv.org/abs/2111.05530

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