{"paper":{"title":"Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, Pedro P\\'erez-Aros","submitted_at":"2021-01-17T16:52:14Z","abstract_excerpt":"This paper is devoted to the study of the expected-integral multifunctions given in the form \\begin{equation*} \\operatorname{E}_\\Phi(x):=\\int_T\\Phi_t(x)d\\mu, \\end{equation*} where $\\Phi\\colon T\\times\\mathbb{R}^n \\rightrightarrows \\mathbb{R}^m$ is a set-valued mapping on a measure space $(T,\\mathcal{A},\\mu)$. Such multifunctions appear in applications to stochastic programming, which require developing efficient calculus rules of generalized differentiation. Major calculus rules are developed in this paper for coderivatives of multifunctions $\\operatorname{E}_\\Phi$ and second-order subdifferent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.06711","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/2101.06711/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"}