{"paper":{"title":"Limiting Stationarity of Regularized Gap-Function Reformulations for Bilevel Optimization with Unbounded Multipliers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jin Zhang, Shangzhi Zeng, Xiaoning Bai","submitted_at":"2026-07-20T10:04:01Z","abstract_excerpt":"Value-function-type reformulations have generated a broad class of methods for bilevel optimization. However, the corresponding value-function-type constraints are inherently degenerate and generally fail to satisfy standard constraint qualifications, so the associated multiplier sequences may be unbounded and bounded-multiplier convergence analyses become inapplicable. We study this issue for the regularized gap-function reformulation of bilevel problems with constrained convex lower-level programs. We prove that accumulation points of approximate stationary sequences are C-stationary for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17772","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/2607.17772/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"}