{"paper":{"title":"A derivative-free $\\mathcal{VU}$-algorithm for convex finite-max problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chayne Planiden, Claudia Sagastiz\\'abal, Warren Hare","submitted_at":"2019-03-26T22:54:11Z","abstract_excerpt":"The $\\mathcal{VU}$-algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain $\\mathcal{V}$-space and its orthogonal $\\U$-space, such that the nonsmoothness of the objective function is concentrated on its projection onto the $\\mathcal{V}$-space, and on the $\\mathcal{U}$-space the projection is smooth. This structure allows for an alternation between a Newton-like step where the function is smooth, and a proximal-point step that is used to find iterates with promising $\\mathcal{VU}$-decompositions. We establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11184","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"}