{"paper":{"title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Kim-Chuan Toh, Kuangyu Ding","submitted_at":"2026-08-07T14:06:54Z","abstract_excerpt":"We prove that mirror descent converges to a KKT point for the nonconvex problem without excluding boundary limits. The result holds under verifiable conditions that jointly couple the objective, the Legendre kernel, and the feasible geometry. The key ingredient to establish the convergence is a metric-flattening reparameterization \\(S\\) that admits a definable boundary extension. Applying the KL argument to the reparameterized objective yields convergence of \\(S(x_k)\\). Continuity of \\(S^{-1}\\) then recovers convergence to the KKT point of the original sequence. We further apply our general fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07248","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/2608.07248/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"}