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

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 direction...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-011-0193-9