A particle swarm pattern search method for bound constrained nonlinear optimization

In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern search method, more speci cally a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search phase of pattern search we apply a particle swarm scheme to globally explore the possible nonconvexity of the objective function. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods also based on function valuesCentro de Matemática da Universidade de Coimbra, Algoritmi Research Center: FCT POCI/MAT/59442/2004, POCI/MAT/58957/200