{"paper":{"title":"Representation of chance-constraints with strong asymptotic guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"IMT), Jean-Bernard Lasserre (LAAS-MAC","submitted_at":"2017-03-10T16:26:38Z","abstract_excerpt":"Given $\\epsilon \\in (0,1)$, a probability measure $\\mu$ on $\\Omega\\subset\\mathbb{R}^p$ and a semi-algebraic set\n$K\\subset X\\times\\Omega$, we consider the feasible set $X^*_\\epsilon=\\{x\\in X:{\\rm Prob}[(x,\\omega)\\in K]\\geq 1-\\epsilon\\}$ associated with  a chance-constraint. We provide a sequence of outer approximations $X^d_\\epsilon=\\{x\\in X: h_d(x)\\geq0\\}$, $d\\in\\mathbb{N}$,  where $h_d$ is a polynomial of degree $d$ whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree $d$. We also obtain the strong and highly desirable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03749","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"}