{"paper":{"title":"Analysis of Limited-Memory BFGS on a Class of Nonsmooth Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Azam Asl, Michael L. Overton","submitted_at":"2018-09-30T01:39:46Z","abstract_excerpt":"The limited memory BFGS (L-BFGS) method is widely used for large-scale unconstrained optimization, but its behavior on nonsmooth problems has received little attention. L-BFGS can be used with or without \"scaling\"; the use of scaling is normally recommended. A simple special case, when just one BFGS update is stored and used at every iteration, is sometimes also known as memoryless BFGS. We analyze memoryless BFGS with scaling, using any Armijo-Wolfe line search, on the function $f(x) = a|x^{(1)}| + \\sum_{i=2}^{n} x^{(i)}$, initiated at any point $x_0$ with $x_0^{(1)}\\not = 0$. We show that if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00292","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":""},"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"}