Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs

Oliver Hinder

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arXiv · 2309.03988

Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs

Oliver Hinder

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Abstract

We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an $\epsilon$-optimal solution in $O( H m_1^{2.5} \sqrt{\textbf{nnz}(A)} \log(H m_2 /\epsilon) )$ matrix-vector multiplies where $m_1$ is the number of constraints, $m_2$ the number of variables, $\textbf{nnz}(A)$ is the number of nonzeros in the constraint matrix, $H$ is the largest absolute coefficient in the right hand side or objective vector, and $\epsilon$ is the distance to optimality of the outputted solution.

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BibTeX RIS

Oliver Hinder. 2023-09-07. Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs. https://arxiv.org/abs/2309.03988

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