On two models for global optimization

• Autorzy: Żilinskas A.
• Konferencja: Evolutionary Computation and Global Optimization (10; Krajowa Konferencja Algorytmy Ewolucyjne i Optymalizacja Globalna; 11-13.06.2007; Będlewo)
• Języki publikacji: EN

Abstrakty

EN

Two models for global optimization are considered: statistical model, and radial basis functions. The equivalence of both models in the case of optimization without noise is discussed. Both models are also evaluated with respect to global optimization in the presence of noise by means of experimental testing where approximation errors of passive one dimensional algorithm are estimated.

Słowa kluczowe

EN

global optimization; algorithms method

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Elektronika
• Rocznik: 2007
• Tom: z. 160
• Strony: 9--16
• Opis fizyczny: Bibliogr. 13 poz., tab.

Twórcy

autor

Żilinskas A.

• Institute of Mathematics and Informatics Vilnius Lithuania,

Bibliografia

• [1] M. Buhmann. Radial Basis Functions: Theory and Implementations. Cambridge University Press, 2003.
• [2] J. Calvin. Nonadaptive univariate optimization for observations with noise. In A. Törn and J. Žilinskas, editors, Models and Algorithms for Global Optimization. Springer, 2007.
• [3] H.-M. Gutman. On the semi norm of radial basis function interpolants. J. Approx. Theor., 111:315-328, 2001.
• [4] H.-M. Gutman. A radial basis function method for global optimization. J. Global Optim., 19:201-227, 2001.
• [5] H. Kushner. A versatile stochastic model of a function of unknown and time-varying form. J. Math. Anal. Appl., 5:150-167, 1962.
• [6] H. Kushner. A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. J. Basic Engineering, 86:97-106, 1964.
• [7] J. Mockus. Bayesian Approach to Global Optimization. KAP, 1988.
• [8] R. G. Regis and Ch. A. Shoemaker. Improved strategies for radial basis function methods for global optimization. J. Global Optim., 37:113-135, 2007.
• [9] M. Stein. Interpolation of Spatial Data, Some Theory of Kriging. Springer, 1999.
• [10] R. Strongin and Y. Sergeyev. Global Optimization with Non-Convex Constraints. Kluwer, 2000.
• [11] A. Törn and A. Žilinskas. Global Optimization. Springer, 1989.
• [12] A. Zilinskas. Axiomatic approach to statistical models and their use in multimodal optimization theory. Math. Program., 22:104-116, 1982.
• [13] A. Zilinskas. Axiomatic characterization of a global optimization algorithm and investigation of its search strategies. Operat. Res. Letters, 4:35-39, 1985.