{"paper":{"title":"Online Packing and Covering Framework with Convex Objectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, Joseph (Seffi) Naor, Niv Buchbinder, Shahar Chen, Viswanath Nagarajan","submitted_at":"2014-12-29T14:09:31Z","abstract_excerpt":"We consider online fractional covering problems with a convex objective, where the covering constraints arrive over time. Formally, we want to solve $\\min\\,\\{f(x) \\mid Ax\\ge \\mathbf{1},\\, x\\ge 0\\},$ where the objective function $f:\\mathbb{R}^n\\rightarrow \\mathbb{R}$ is convex, and the constraint matrix $A_{m\\times n}$ is non-negative. The rows of $A$ arrive online over time, and we wish to maintain a feasible solution $x$ at all times while only increasing coordinates of $x$. We also consider \"dual\" packing problems of the form $\\max\\,\\{c^\\intercal y - g(\\mu) \\mid A^\\intercal y \\le \\mu,\\, y\\ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8347","kind":"arxiv","version":1},"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"}