Global Optimization using a Dynamical Systems Approach |
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Authors: | Stefan Sertl Michael Dellnitz |
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Institution: | (1) Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, D-33095 Paderborn, Germany |
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Abstract: | We develop new algorithms for global optimization by combining well known branch and bound methods with multilevel subdivision
techniques for the computation of invariant sets of dynamical systems. The basic idea is to view iteration schemes for local
optimization problems – e.g. Newton’s method or conjugate gradient methods – as dynamical systems and to compute set coverings
of their fixed points. The combination with bounding techniques allow for the computation of coverings of the global optima
only. We show convergence of the new algorithms and present a particular implementation.
Michael Dellnitz - Research of the authors is partially supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich
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Keywords: | Branch and bound optimization Computation of fixed points Dynamical systems Global optimization |
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