{"paper":{"title":"Smooth minimization of nonsmooth functions with parallel coordinate descent methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.DC","authors_text":"Olivier Fercoq, Peter Richt\\'arik","submitted_at":"2013-09-23T17:24:00Z","abstract_excerpt":"We study the performance of a family of randomized parallel coordinate descent methods for minimizing the sum of a nonsmooth and separable convex functions. The problem class includes as a special case L1-regularized L1 regression and the minimization of the exponential loss (\"AdaBoost problem\"). We assume the input data defining the loss function is contained in a sparse $m\\times n$ matrix $A$ with at most $\\omega$ nonzeros in each row. Our methods need $O(n \\beta/\\tau)$ iterations to find an approximate solution with high probability, where $\\tau$ is the number of processors and $\\beta = 1 +"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5885","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"}