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Local optimization method with global multidimensional search. (English) Zbl 1123.90079

Summary: 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 algorithms 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.

MSC:

90C56 Derivative-free methods and methods using generalized derivatives
90C26 Nonconvex programming, global optimization
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References:

[1] Andramonov, M.Y., Rubinov, A.M., Glover, B.M. (1997). Cutting angle method for minimizing increasing convex-along-rays functions, Research Report 97/7, SITMS, University of Ballarat
[13] Blake, C.L., Merz, C.J. (1998). UCI Repository of machine learning databases, Department of Information and Computer Science, University of Calirfornia, Irvine. Also available at: http://www.ics.uci.edu/mlearn/MLRepository.html
[15] Brimberg J., Love R.F., Mehrez A. (2002). Location/Allocation of queuing facilities in continuous space using minsum and minmax criteria. In: Pardalos P., Migdalas A., Burkard R. (ed.). Combinatorial and Global Optimization, World Scientific · Zbl 1030.90046
[18] Hansen, P., Ngai, E., Cheung, B.K., Mladenovic, N. (August, 2002). Analysis of global k-means, an incremental heuristic for minimum sum-of-squares clustering, Les Cahiers du GERAD, G-2002-43 · Zbl 1336.62182
[23] Neumaier, A., Optimization test problems. Available in: solon.cma.univie.ac.at/neum/glopt.html
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