{"paper":{"title":"Minimizing a low-dimensional convex function over a high-dimensional cube","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.OC","authors_text":"Christoph Hunkenschr\\\"oder, Robert Weismantel, Sebastian Pokutta","submitted_at":"2022-04-11T17:13:14Z","abstract_excerpt":"For a matrix $W \\in \\mathbb{Z}^{m \\times n}$, $m \\leq n$, and a convex function $g: \\mathbb{R}^m \\rightarrow \\mathbb{R}$, we are interested in minimizing $f(x) = g(Wx)$ over the set $\\{0,1\\}^n$. We will study separable convex functions and sharp convex functions $g$. Moreover, the matrix $W$ is unknown to us. Only the number of rows $m \\leq n$ and $\\|W\\|_{\\infty}$ is revealed. The composite function $f(x)$ is presented by a zeroth and first order oracle only. Our main result is a proximity theorem that ensures that an integral minimum and a continuous minimum for separable convex and sharp con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.05266","kind":"arxiv","version":2},"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/2204.05266/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"}