On Acceleration of Derivative-Free Univariate Lipschitz Global Optimization Methods
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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.
KeywordsLipschitz global optimization Univariate black-box functions Geometric and information approaches Local tuning
The work of M.S. Mukhametzhanov was supported by the INdAM-GNCS funding “Giovani Ricercatori 2018–2019”.
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