Stochastic discrete optimization using a surrogate problem methodology

We consider stochastic discrete optimization problems where the decision variables are non-negative integers. We propose and analyze an online control scheme which transforms the problem into a "surrogate" continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both actual and surrogate system states. Convergence of the proposed algorithm is established and it is shown that the discrete state neighborhood of the optimal surrogate state contains the optimal solution of the original problem. Numerical results are included in the paper illustrating the fast convergence properties of this approach.