2012, 2(1): 69-90. doi: 10.3934/naco.2012.2.69

Univariate geometric Lipschitz global optimization algorithms

1. 

DEIS, University of Calabria, Via P. Bucci, Cubo 42C, 87036 -- Rende (CS), Italy, Italy

Received  May 2011 Revised  August 2011 Published  March 2012

In this survey, univariate global optimization problems are considered where the objective function or its first derivative can be multiextremal black-box costly functions satisfying the Lipschitz condition over an interval. Such problems are frequently encountered in practice. A number of geometric methods based on constructing auxiliary functions with the usage of different estimates of the Lipschitz constants are described in the paper.
Citation: Dmitri E. Kvasov, Yaroslav D. Sergeyev. Univariate geometric Lipschitz global optimization algorithms. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 69-90. doi: 10.3934/naco.2012.2.69
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