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Simplicial Global Optimization pp 61–86Cite as

Simplicial Lipschitz Optimization Without Lipschitz Constant

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Abstract

Global optimization algorithms discussed in the previous chapter, use the global estimate of the Lipschitz constant L given a priori and do not take into account the local information about the behavior of the objective function over every small subregion of \(\mathbb{D}\). It has been demonstrated in [74, 116, 126, 134] that estimation of the local Lipschitz constants during the search allows significant acceleration of the global search. Naturally, balancing between the local and global information must be performed in an appropriate way to increase the speed of optimization and avoid the missing of the global solution.

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  1. Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Remigijus Paulavičius & Julius Žilinskas

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  1. Remigijus Paulavičius
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  2. Julius Žilinskas
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© 2014 Remigijus Paulavičius, Julius Žilinskas

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Paulavičius, R., Žilinskas, J. (2014). Simplicial Lipschitz Optimization Without Lipschitz Constant. In: Simplicial Global Optimization. SpringerBriefs in Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9093-7_3

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