{"paper":{"title":"Bridging Identification and Second-Order Acceleration: A Fast Alternating Minimization Framework for Composite Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Min Tao, Zihao Xia","submitted_at":"2026-06-23T14:02:43Z","abstract_excerpt":"We consider a class of composite optimization problems involving a smooth function and a proper, lower semicontinuous regularizer, which may be nonconvex and nonsmooth.\n  We propose a novel alternating minimization framework that integrates proximal-gradient steps with cubic-regularized Newton updates restricted to a dynamically identified low-dimensional subspace.\n  Under the Kurdyka--{\\L}ojasiewicz (KL) property, we establish global convergence of the proposed method to a stationary point.\n  Moreover, by incorporating an adaptive thresholding strategy guided by the KL exponent, we prove a fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24600","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24600/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"}