New computer methods for global optimization
New computer methods for global optimization
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
A Note on the Griewank Test Function
Journal of 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.