Stochastic optimisation with inequality constraints using simultaneous perturbations and penalty functions

We present a stochastic approximation algorithm based on penalty function method and a simultaneous perturbation gradient estimate for solving stochastic optimisation problems with general inequality constraints. We present a general convergence result that applies to a class of penalty functions including the quadratic penalty function, the augmented Lagrangian, and the absolute penalty function. We also establish an asymptotic normality result for the algorithm with smooth penalty functions under minor assumptions. Numerical results are given to compare the performance of the proposed algorithm with different penalty functions.