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October  2009, 5(4): 825-834. doi: 10.3934/jimo.2009.5.825

The modified cutting angle method for global minimization of increasing positively homogeneous functions over the unit simplex

Burak Ordin 1,

1. 

Ege University, Faculty of Science, Department of Mathematics, 35100, Bornova, Izmir, Turkey

Received  September 2008 Revised  June 2009 Published  August 2009

The paper deals with a method for global minimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. A new approach for solving the auxiliary problem in the cutting angle method is proposed. In the method, the auxiliary problem is reformulated as a certain combinatorial problem. The modified version of the cutting angle method is also applied for Lipschitz functions that could be expressed as increasing positively homogeneous functions. We report results of numerical experiments which demonstrate that the proposed algorithm is very efficient in the search for a global minimum.
Keywords: global optimization, cutting angle method, dominating subset with minimal weight problem., increasing positively homogeneous function, lipschitz function.
Mathematics Subject Classification: Primary: 90C, 65K; Secondary: 49.
Citation: Burak Ordin. The modified cutting angle method for global minimization of increasing positively homogeneous functions over the unit simplex. Journal of Industrial and Management Optimization, 2009, 5 (4) : 825-834. doi: 10.3934/jimo.2009.5.825
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