Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization
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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.
KeywordsGlobal optimization Derivative-free optimization Direct-search methods Search step Radial basis functions d.c. programming DCA
Mathematics Subject Classification (2000)90C26 90C30 90C56
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- Le Thi HA, Pham Dinh T (1997) Convex analysis approach to d.c. programming: theory, algorithms and applications. Acta Math Vietnam 22:289–355 Google Scholar
- Käck J-E (2004) Constrained global optimization with radial basis functions. Technical report research report MdH-IMa-2004, Department of Mathematics and Physics, Mälardalen University, Västerås, Sweden Google Scholar
- Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs, 3rd edn. Springer, Berlin Google Scholar
- Oeuvray R (2005) Trust-region methods based on radial basis functions with application to biomedical imaging. PhD thesis, Institut de Mathématiques, École Polytechnique Fédérale de Lausanne, Switzerland Google Scholar
- Oeuvray R, Bierlaire M (2009) BOOSTERS: a derivative-free algorithm based on radial basis functions. Int J Model Simul 29:4634–4636 Google Scholar
- Parsopoulos KE, Plagianakos VP, Magoulas GD, Vrahatis MN (2001) Stretching technique for obtaining global minimizers through particle swarm optimization. In: Proc of the particle swarm optimization workshop, Indianapolis, USA, pp 22–29 Google Scholar
- Pham Dinh T, Elbernoussi S (1988) Duality in d.c. (difference of convex functions) optimization. In: Subgradient methods, vol 84. Birkhäuser, Basel, pp 276–294 Google Scholar
- Wild SM, Shoemaker CA (2011) Global convergence of radial basis function trust region derivative-free algorithms. SIAM J Optim. doi: 10.1137/09074927x