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Global optimization using a dynamical systems approach. (English) Zbl 1149.90427
Summary: 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.
MSC:
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
37N40Dynamical systems in optimization and economics
90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
90C52Methods of reduced gradient type
90C53Methods of quasi-Newton type
Software:
INTOPT_90
References:
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