Journal of Global Optimization

, Volume 45, Issue 1, pp 95–110

Convergence analysis of a global optimization algorithm using stochastic differential equations

Article

DOI: 10.1007/s10898-008-9397-4

Cite this article as:
Parpas, P. & Rustem, B. J Glob Optim (2009) 45: 95. doi:10.1007/s10898-008-9397-4

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 (Π) 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 Π.

Keywords

Stochastic global optimization Simulated annealing Stochastic differential equations Fokker-Planck equation Laplace’s method Projection algorithms 

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Department of ComputingImperial CollegeLondonUK

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