{"paper":{"title":"Online Convex Covering and Packing Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ning Kang, T-H. Hubert Chan, Zhiyi Huang","submitted_at":"2015-02-06T05:33:10Z","abstract_excerpt":"We study the online convex covering problem and online convex packing problem. The (offline) convex covering problem is modeled by the following convex program: $\\min_{x \\in R_+^n} f(x) \\ \\text{s.t}\\ A x \\ge 1$, where $f : R_+^n \\mapsto R_+$ is a monotone and convex cost function, and $A$ is an $m \\times n$ matrix with non-negative entries. Each row of the constraint matrix $A$ corresponds to a covering constraint. In the online problem, each row of $A$ comes online and the algorithm must maintain a feasible assignment $x$ and may only increase $x$ over time. The (offline) convex packing probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01802","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":""},"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"}