Stochastic Optimization for System Design

Optimization problems occur in system designs with simulation applications. The decision variables are controllable system parameters of interest and the objective function is a system performance measure that can be estimated via simulation experiments. Using the estimates of objective function values to find the optimal point is called the stochastic optimization problem. The literature of such problems focuses on stochastic approximation. Despite its convergence proof, stochastic approximation may converge slowly if the algorithm parameter values are not well chosen. For practical uses, good algorithms should provide real-time solutions besides guaranteeing convergence. We propose the FDRA algorithm assuming that the objective function is differentiable. FDRA uses the RA-Broyden's algorithm to find the zero of the gradient function, where gradients are estimated by the finite-difference method. In our empirical results, FDRA converges quickly and is robust to its algorithm parameters.