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Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization

An Le Thi Hoai(lethi***at***univ-metz.fr)
A. I. F. Vaz(aivaz***at***dps.uminho.pt)
L. N. Vicente(lnv***at***mat.uc.pt)

Abstract: In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems.

Keywords: Global optimization, derivative-free optimization, direct-search methods, search step, radial basis functions, d.c. programming, DCA.

Category 1: Global Optimization

Category 2: Nonlinear Optimization

Citation: Le Thi Hoai An, A. I. F. Vaz, and L. N. Vicente, Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization, preprint 09-37, Dept. of Mathematics, Univ. Coimbra.

Download: [PDF]

Entry Submitted: 10/12/2009
Entry Accepted: 10/12/2009
Entry Last Modified: 10/12/2009

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