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2020 | OriginalPaper | Buchkapitel

Multiextremal Optimization in Feasible Regions with Computable Boundaries on the Base of the Adaptive Nested Scheme

verfasst von : Victor Gergel, Vladimir Grishagin, Ruslan Israfilov

Erschienen in: Numerical Computations: Theory and Algorithms

Verlag: Springer International Publishing

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Abstract

The paper is devoted to consideration of multidimensional optimization problems with multiextremal objective functions over search domains determined by constraints, which form a special type of domain boundaries called computable ones, which, in general case, are non-linear and multiextremal. The regions of this class can be very complicated, in particular, non-convex, non-simply connected, and even disconnected. For solving such problems, a new global optimization technique based on the adaptive nested scheme developed recently for unconstrained optimization is proposed. The novelty consists in combination of the adaptive scheme with a technique for reducing the constraints to an explicit form of feasible subregions in internal subproblems of the nested scheme that allows one to evaluate the objective function at the feasible points only. For efficiency estimation of the proposed adaptive nested algorithm in comparison with the classical nested optimization and the penalty function method, a representative numerical experiment on the test classes of multidimensional multiextremal functions has been carried out. The results of the experiment demonstrate a significant advantage of the adaptive scheme over its competitors.

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Vorheriges Kapitel Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields

Nächstes Kapitel On Polyhedral Estimates of Reachable Sets of Discrete-Time Systems with Uncertain Matrices and Integral Bounds on Additive Terms

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Titel: Multiextremal Optimization in Feasible Regions with Computable Boundaries on the Base of the Adaptive Nested Scheme
verfasst von: Victor Gergel
Vladimir Grishagin
Ruslan Israfilov
Verlag: Springer International Publishing
Buch: Numerical Computations: Theory and Algorithms
Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-40616-5_9

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