Abstract
Existing approaches to multiextremal optimization (see Evtushenko, 1971; Ivanov, 1972; Mockus, 1977; Strongin, 1978; Zilinskas, 1978) mostly focus on numerical methods for unconstrained problems. Constraints are usually handled by introducing penalty functions since other techniques (see, for example, Demyanov and Vasiliev, 1981) require the minimizing function and the constraints.to be convex, unimodal, or to have other properties. Below we pre sent a new algorithm for multiextremal problems with nonconvex constraints which does not make use of penalties.
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References
Evtushenko, Yu.G. (1971). Numerical method for seeking the global extremum of a function (nonuniform grid search). Journal of Computational Mathematics and Mathematical Physics, 11: 1390–1403 (in Russian).
Ivanov, V.V. (1972). On optimal minimization algorithms for functions of some classes. Kibernetika, (4): 81–94 (in Russian).
Mockus, J. (1977). On Bayesian methods of seeking the extremum and their applications. In Gilchrist (Ed.), Information Processing 77. North-Holland, Amsterdam, pp. 195–200.
Demyanov, V.F. and Vasiliev, L.V. (1981). Nondifferentiable Optimization. Nauka, Moscow (in Russian).
Strongin, R.G. (1978). Numerical Methods in Multiextremal Problems. Nauka, Moscow (in Russian).
Zilinskas, A. (1978). On one-dimensional multimodal minimization. In Transactions of the Eighth Prague Conference on Information Theory, Stat. Dec. Functions, and Random Processes, pp. 393–402.
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© 1985 Springer-Verlag Berlin Heidelberg
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Strongin, R.G. (1985). Numerical Methods for Multiextremal Nonlinear Programming Problems with Nonconvex Constraints. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_25
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DOI: https://doi.org/10.1007/978-3-662-12603-5_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15979-7
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