We present a novel application of the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm (Spall, 2000) to optimize knot probabilities for a simple cubic lattice self-avoiding polygon model (Tesi et al., 1994), of DNA knotting experiments (Shaw and Wang, 1993). The SPSA algorithm is an efficient iteration method for optimizing a multivariable objective function when function values are only available via statistical estimates such as from Markov chain Monte Carlo (MCMC) simulations. A key feature of the SPSA algorithm is that only two evaluations of the objective function are required to obtain updates at each iteration, regardless of problem dimension. We review the SPSA algorithm and then apply it to a lattice polygon model of circular DNA where MCMC is used to generate random polygon conformations in order to estimate knot probabilities as a function of salt concentration.