A Global Optimization Algorithm for Multivariate Functionswith Lipschitzian First Derivatives

Authors:
Victor P. Gergel
Affiliations:
Software Department, University of Nizhni Novgorod, Gagarin Ave., 23, Nizhni Novgorod, 603600, Russia
Venue:
Journal of Global Optimization
Year:
1997

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Abstract

In this paper we propose a new multi-dimensional methodto solve unconstrained global optimization problems with Lipschitzianfirst derivatives. The method is based on apartition scheme that subdivides the search domain into a set of hypercubesin the course of optimization. This partitioning is regulated by thedecision rule that provides evaluation of the "importance"of each generated hypercube and selection of some partition element to performthe next iteration. Sufficient conditions of global convergence for the newmethod are investigated. Results of numerical experiments are alsopresented.