Robust approximation of chance constrained optimization with polynomial perturbation

This paper studies a robust approximation method for solving a class of chance constrained optimization problems. The constraints are assumed to be polynomial in the random vector. Under the assumption, the robust approximation of the chance constrained optimization problem can be reformulated as an optimization problem with nonnegative polynomial conic constraints. A semidefinite relaxation algorithm is proposed for solving the approximation. Its asymptotic and finite convergence are proven under some mild assumptions. In addition, we give a framework for constructing good uncertainty sets in the robust approximation. Numerical experiments are given to show the efficiency of our approach.Comment: 25 page