{"paper":{"title":"Distributionally robust polynomial chance-constraints under mixture ambiguity sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean Lasserre (LAAS-MAC), Tillmann Weisser (LAAS-MAC)","submitted_at":"2018-03-30T15:08:10Z","abstract_excerpt":"Given $X \\subset R^n$, $\\varepsilon \\in (0,1)$, a parametrized family of probability distributions $(\\mu\\_{a})\\_{a\\in A}$ on $\\Omega\\subset R^p$, we consider the feasible set $X^*\\_\\varepsilon\\subset X$ associated with  the {\\em distributionally robust} chance-constraint \\[X^*\\_\\varepsilon\\,=\\,\\{x \\in X :\\:{\\rm Prob}\\_\\mu[f(x,\\omega)\\,>\\,0]> 1-\\varepsilon,\\,\\forall\\mu\\in M\\_a\\},\\]where $M\\_a$ is the set of all possibles mixtures of distributions $\\mu\\_a$, $a\\in A$.For instance and typically, the family$M\\_a$ is the set of all mixtures ofGaussian distributions on $R$ with mean and standard devi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11500","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":""},"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"}