Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets

This talk addresses the  “chance constrained problems”, optimization problems with probabilistic constraints, and also "chance optimization" 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 also sum of squares is provided, whose sequence of optimal values is 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.