- Representation of distributionally robust chance-constraints Jean B Lasserre(lasserrelaas.fr) Tillmann Weisser(tweisserlaas.fr) Abstract: 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 $X^*_\varepsilon\,=\,\{x\in X:\:{\rm Prob}_\mu[f(x,\omega)\,>\,0]> 1-\varepsilon,\,\forall\mu\in\mathscr{M}_a\},$ where $\mathscr{M}_a$ is the set of all possibles mixtures of distributions $\mu_a$, $a\in A$. For instance and typically, the family $\mathscr{M}_a$ is the set of all mixtures of Gaussian distributions on $R$ with mean and standard deviation $a=(a,\sigma)$ in some compact set $A\subset R^2$. We provide a sequence of inner approximations $X^d_\varepsilon=\{x\in X:w_d(x) <\varepsilon\}$, $d\in \mathbb{N}$, where $w_d$ 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 $\lambda(X^*_\varepsilon\setminus X^d_\varepsilon)\to0$ as $d$ increases, where $\lambda$ is the Lebesgue measure on $X$. Same results are also obtained for the more intricated case of distributionally robust joint" chance-constraints. Keywords: Chance-constraints; distributionally robust; semidefinite relaxations Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 3: Stochastic Programming Citation: LAAS-CNRS, 7 avenue du Colonel Roche, 31031 Toulouse, France Download: [PDF]Entry Submitted: 04/20/2018Entry Accepted: 04/20/2018Entry Last Modified: 04/20/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.