Local Optimization Method with Global Multidimensional

Adil Bagirov (a.bagirovballarat.edu.au)
Alex Rubinov (a.rubinovballarat.edu.au)
Jiapu Zhang (jzhangstudents.ballarat.edu.au)

Abstract: This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and with the so-called cluster function. These results confirm that the proposed algorithm allows one to find a global minimizer or at least a deep local minimizer of a function with a huge amount of shallow local minima.

Keywords: Global optimization, discrete gradient, derivative-free optimization, the cutting angle method, Lipschitz programming

Category 1: Global Optimization

Citation: Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria 3353, Australia, December 2003

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Entry Submitted: 12/23/2003
Entry Accepted: 01/05/2004
Entry Last Modified: 12/23/2003

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