{"paper":{"title":"Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Oliver Hinder","submitted_at":"2023-09-07T19:43:32Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.03988","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.03988/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}