Abstract
In recent papers of the author a general class of algorithms was proposed to solve the global optimization problem inn dimensions (n≥1). Here we show that certain types of univariate methods (n=1) can be generalized in a straightforward manner to obtain algorithms for the casen>1. Some numerical test tesults are also reported.
Zusammenfassung
In vorangehenden Arbeiten stelle der Autor eine allgemeine Klasse von Verfahren zur Lösung des Problems der globalen Optimierung inn (n≥1) Dimensionen vor. In dieser Arbeit wird gezeigt, daß einige Typen von univariaten Methoden (n=1) sich direkt verallgemeinern lassen auf den Falln>1. Über numerische Erfahrungen wird berichtet.
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Archetti, F.: Analysis of stochastic strategies for the numerical solution of the global optimization problem. In: Numerical Techniques for Stochastic Systems (Archetti, F., Cugiani, M., eds.), pp. 275–295. Amsterdam: North-Holland 1980.
Archetti, F., Betro, B.: A probabilistic algorithm for global optimization. Calcolo 16,3, 335–343 (1979).
Boender, C. G. E., Rinnooy Kan, A. H. G., Stougie, L., Timmer, G. T.: A stochastic method for global optimization. Mathematical Programming22, 125–140 (1982).
Danilin, Yu. M., Pijavskij, S. A.: An algorithm for finding the absolute minimum. In: Theory of Optimal Decisions, Vol. 2, pp. 13–24 (in Russian). Inst. Cybernetics of the Ukrainian Acad. Sci., Kiev (1967).
Dixon, L. C. W., Szegő, G. P. (eds.): Towards Global Optimisation, Vol. I–II. Amsterdam: North-Holland 1975, 1978.
Kushner, H.: A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Trans. ASME, Series D, J. Basic Eng.86, 97–105 (1964).
Mockus, J., Tiesis, V., Zilinskas, A.: The application of Bayesian methods for seeking the extremum, pp. 117–129. In: [4], Vol. 2.
Pintér, J.: A unified approach to globally convergent one-dimensional optimization algorithms. Techn, report IAMI 83-5. Inst. Appl. Math. Inf. CNR, Milan (1983).
Pintér, J.: Convergence properties of stochastic optimization procedures. Math. Operationsforsch. u. Stat. Ser. Opt.15, 405–427 (1984a).
Pintér, J.: Globally convergent methods forn-dimensional multiextremal optimization. Math. Operationsforsch. u. Stat. Ser. Opt. (to appear) (1984b).
Shubert, B. O.: A sequential method seeking the global maximum of a function. SIAM Journal on Numerical Analysis9, 379–388 (1972).
Strongin, R. G.: Numerical methods for multiextremal problems (in Russian). Nauka, Moscow (1978).
Zilinskas, A.: One-step Bayesian method for seeking the extremum of a univariate function (in Russian). Cybernetics1, 139–144 (1975).
Zilinskas, A.: Two algorithms for one-dimensional multimodal minimization. Math. Operationsforsch. u. Stat. Ser. Opt.12, 53–63 (1981).
Zilinskas, A.: Axiomatic approach to statistical models and their use in multimodal optimization theory. Mathematical Programming22, 104–116 (1982).
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Pintér, J. Extended univariate algorithms for n-dimensional global optimization. Computing 36, 91–103 (1986). https://doi.org/10.1007/BF02238195
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DOI: https://doi.org/10.1007/BF02238195