2 research outputs found
Representation of chance-constraints with strong asymptotic guarantees
International audienceGiven e â (0, 1), a probability measure ” on ⊠â Rp and a semi-algebraic set K â X Ă âŠ, we consider the feasible set X(e) = {x â X : Prob[(x, Ï) â K] â„ 1 â e } associated with a chance-constraint. We provide a sequence outer approximations X_d(e) = {x â X : h_d (x) â„ 0}, d â 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 asymptotic guarantee that λ(X_d(e) \X (e)) â 0 as d increases, where λ is the Lebesgue measure on X. Finallu inner approximations with same asymptotic guaranties are also obtained by considering the complement