Penalty function methods for constrained stochastic approximation

This paper is concerned with sequential Monte Carlo methods for optimizing a system under constraints. We wish to minimize f(x), where qⁱ(x) ? 0 (i = 1, …, m) must hold. We can calculate the qⁱ(x), but f(x) can only be observed in the presence of noise. A general approach, based on an adaptation of a version of stochastic approximation to the penalty function method, is discussed and a convergence theorem is proved.