Univariate box-constrained global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous and multiextremal. It is assumed that its analytical representation is unknown (the function is given as a “black-box”) and even one its evaluation is a computationally expensive procedure. Geometric and information statistical frameworks for construction of global optimization algorithms are discussed. Several powerful acceleration techniques are described and a number of methods of both classes is constructed by mixing the introduced acceleration ideas. Numerical experiments executed on broad test classes taken from the literature show advantages of the presented techniques with respect to their direct competitors.

On acceleration of derivative-free univariate Lipschitz global optimization methods

Kvasov Dmitry
Writing – Review & Editing
;
Mukhametzhanov Marat
Membro del Collaboration Group
;
Nasso Maria Chiara
Writing – Original Draft Preparation
;
Sergeev Yaroslav
Supervision
2020

Abstract

Univariate box-constrained global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous and multiextremal. It is assumed that its analytical representation is unknown (the function is given as a “black-box”) and even one its evaluation is a computationally expensive procedure. Geometric and information statistical frameworks for construction of global optimization algorithms are discussed. Several powerful acceleration techniques are described and a number of methods of both classes is constructed by mixing the introduced acceleration ideas. Numerical experiments executed on broad test classes taken from the literature show advantages of the presented techniques with respect to their direct competitors.
978-3-030-40615-8
Blck-box global optimization
Numerical Analysis
Geometric and information approaches
Acceleration techniques
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/299100
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