Via Zoom: Moment-Sum-Of-Squares based Semidefinite Programming for Chance Constrained Optimization

This talk addresses “chance-constrained optimization" problems with probabilistic polynomial constraints and also "chance optimization" problems where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective of developing systematic numerical procedures to solve such problems, a sequence of convex relaxations based on the theory of measures and moments and theory of sum of squares polynomials is provided, whose sequence of optimal values are shown to converge to the optimal value of the original problem. Indeed, we provide a sequence of semidefinite programs of increasing dimension which can arbitrarily approximate the solution of the original problem.