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Stochastic Approximation Algorithms With Applications To Particle Swarm Optimization, Adaptive Optimization, And Consensus, Quan Yuan

Wayne State University Dissertations

In this dissertation, we present three problems arising in recent applications of stochastic approximation methods. In Chapter 2, we use stochastic approximation to analyze Particle Swarm Optimization (PSO) algorithm. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence method. A centered and scaled sequence of the estimation errors is shown …