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

• Published in: TOP Vol. 20; no. 1; pp. 190 - 214
• Main Authors: Le Thi, H. A., Vaz, A. I. F., Vicente, L. N.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2012; Springer; Springer Verlag
• Subjects: Business and Management; Computer Science; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Industrial and Production Engineering; Insurance; Management; Operations Research/Decision Theory; Optimization; Original Paper; Statistics for Business; Global optimization; Radial basis functions; DCA; 90C30; 90C56; d.c. programming; Search step; 90C26; Direct-search methods; Derivative-free optimization
• ISSN: 1134-5764; 1863-8279
• DOI: 10.1007/s11750-011-0193-9

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.