Convergence analysis of a global optimization algorithm using stochastic differential equations

We establish the convergence of a stochastic global optimization algorithm for general non-convex, smooth functions. The algorithm follows the trajectory of an appropriately defined stochastic differential equation (SDE). In order to achieve feasibility of the trajectorywe introduce information from the Lagrangemultipliers into the SDE. The analysis is performed in two steps. We first give a characterization of a probability measure ( ) that is defined on the set of global minima of the problem. We then study the transition density associated with the augmented diffusion process and show that its weak limit is given by .