{"paper":{"title":"Stochastic Block Mirror Descent Methods for Nonsmooth and Stochastic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Cong D. Dang, Guanghui Lan","submitted_at":"2013-09-09T18:33:15Z","abstract_excerpt":"In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significantly reduce the cost per iteration of the latter algorithm. We establish the rate of convergence of the SBMD method along with its associated large-deviation results for solving general nonsmooth and stochastic opti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2249","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"}