{"paper":{"title":"A note on stationarity in constrained optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Edouard Pauwels (TSE-R)","submitted_at":"2024-02-15T09:48:59Z","abstract_excerpt":"Minimizing a smooth function f on a closed subset C leads to different notions of stationarity: Fr{\\'e}chet stationarity, which carries a strong variational meaning, and criticality, which is defined through a closure process and involves the notion of limiting, or Mordukovitch, subdifferential. The latter is an optimality condition which may loose the variational meaning of Fr{\\'e}chet stationarity in some settings. The purpose of this note is to illustrate that, while criticality is the appropriate notion in full generality, Fr{\\'e}chet stationarity is typical in practical scenarios.We gathe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.09831","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.09831/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"}