{"paper":{"title":"Generalized differentiation with positively homogeneous maps: Applications in set-valued analysis and metric regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"C.H. Jeffrey Pang","submitted_at":"2009-07-31T18:43:19Z","abstract_excerpt":"We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between the Aubin property and coderivatives, and study how metric regularity and open covering can be refined to have a directional property similar to our concept of generalized differentiation. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5439","kind":"arxiv","version":5},"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"}