A modification of the DIRECT method for Lipschitz global optimization for a symmetric function

Authors:
Ratko Grbić;Emmanuel Karlo Nyarko;Rudolf Scitovski
Affiliations:
Faculty of Electrical Engineering, University of Osijek, Osijek, Croatia 31 000;Faculty of Electrical Engineering, University of Osijek, Osijek, Croatia 31 000;Department of Mathematics, University of Osijek, Osijek, Croatia 31 000
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function. An efficient modification of the well-known DIRECT (DIviding RECTangles) method called SymDIRECT is proposed for solving this problem. The method is illustrated and tested on several standard test functions. The application of this method to solving complex center-based clustering problems for the data having only one feature is particularly presented.