{"paper":{"title":"Dual Prices for Frank--Wolfe Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"G\\'abor Braun, Sebastian Pokutta","submitted_at":"2021-01-06T15:16:52Z","abstract_excerpt":"In this note we observe that for constrained convex minimization problems $\\min_{x \\in P}f(x)$ over a polytope $P$, dual prices for the linear program $\\min_{z \\in P} \\nabla f(x) z$ obtained from linearization at approximately optimal solutions $x$ have a similar interpretation of rate of change in optimal value as for linear programming, providing a convex form of sensitivity analysis. This is of particular interest for Frank--Wolfe algorithms (also called conditional gradients), forming an important class of first-order methods, where a basic building block is linear minimization of gradient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.02087","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/2101.02087/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"}