Abstract
A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.
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References
Archetti, F. and Betro, B. (1979), A Probabilistic Algorithm for Global Optimization, Calcolo 16, 335–343.
Fine, T. (1973), Theories of Probability, AP, NY.
Kushner, H. (1964), A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise, Trans. ASME, ser. D 86(1), 97–105.
Mockus, J. (1972), On Bayesian Methods of Search for Extremum, Automatics and Computers 3, 53–62.
Mockus, J. (1989), Bayesian Approach to Global Optimization, Kluwer, Dordrecht.
Neimark, J. and Strongin, R. (1969), Informational Approach to the Problem of Search for Extremum of a Function, Engineering Cybernetics 4, 17–26.
Strongin, R. (1978), Numerical Methods of Multimodal Optimization, Nauka, Moskow.
Ŝaltenis, V. (1971), On a Method for Multimodal Optimization, Automatics and Computers 3, 33–38.
Törn, A. and Žilinskas, A. (1989), Global Optimization, Springer, Berlin.
Žilinskas, A. (1976), A Method of One-Dimensional Multiextremal Minimization, Engineering Cybernetics, 71–74.
Žilinskas, A. (1978), Optimization of One-Dimensional Multimodal Functions, Algorithm AS 133, Applied Statistics 23, 367–375.
Žilinskas, A. (1979), Axiomatic Approach to Extrapolation Problem under Uncertainty, Automatics and Remote Control 12, 66–70.
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Žilinskas, A. A review of statistical models for global optimization. J Glob Optim 2, 145–153 (1992). https://doi.org/10.1007/BF00122051
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DOI: https://doi.org/10.1007/BF00122051