Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 34, Issue 4, Pages 569-587Publisher
SPRINGER
DOI: 10.1007/s10898-005-4384-5
Keywords
branch and bound optimization; computation of fixed points; dynamical systems; global optimization
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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.
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