Discrete Stochastic Approximation with Application to Resource Allocation

n optimization problem involves fi nding the best value of an objective function or fi gure of merit—the value that optimizes the function. If the set of options is fi nite in number, then the problem is discrete. If the value of the objective function is uncertain because of measurement noise or some other source of random variation, the problem is stochastic. Mathematically, the discrete optimization problem is a nonlinear optimization problem involving integer variables, and its solution will require some iterative procedure. This article discusses one such procedure for solving diffi cult optimization problems. The procedure is a discrete-variables version of the Simultaneous Perturbation Stochastic Approximation algorithm, developed at APL, for solving optimization problems involving continuous variables. The discrete-variables algorithm shares some of the computational effi ciency of its continuous counterpart.