Convergence analysis of a global optimization algorithm using stochastic differential equations

Authors:
Panos Parpas;Berç Rustem
Affiliations:
Department of Computing, Imperial College, London, UK SW7 2AZ;Department of Computing, Imperial College, London, UK SW7 2AZ
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

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 trajectory we introduce information from the Lagrange multipliers into the SDE. The analysis is performed in two steps. We first give a characterization of a probability measure (驴) 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 驴.