Constrained Optimization via Stochastic Approximation with a Simultaneous Perturbation Gradient Approximation

Abstract

The paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions of the optimization parameters. It is shown that under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point. The procedure is illustrated by a numerical example.