{"paper":{"title":"Sequential and exact formulae for the subdifferential of nonconvex integral functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abderrahim Hantoute, Pedro P\\'erez-Aros, Rafael Correa","submitted_at":"2018-03-14T21:52:16Z","abstract_excerpt":"This work concerns the study of the subdifferential of the integral functional\n  $$\n  E_f(x)=\\int_{T} f(t,x)d\\mu(t),\n  $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\\mathcal{A},\\mu)$ is a $\\sigma$-finite measure space, while the decision variables vary in a separable Asplund space.\n  First, using techniques of variational analysis we establish sequential approximate formulae for the Fr\\'echet subdifferential of $E_f$. Secondly, we introduce a Lipschitz-like condition, which allows us to give an upper-estimation for the limiting subdifferential of $E_{f}$ even when this fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05521","kind":"arxiv","version":3},"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"}