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Stochastic methods for global optimization. (English) Zbl 0556.90073
The search for the global minimum of a real-valued function of many variables is considered. The problem is supposed to be unconstrained. The random methods for this problem are reviewed. Some approaches to estimate the minimum value from the random samples are discussed, e.g. based on an asymptotic expression for the p-level confidence interval, extrapolation of the \(\psi\)-function and the Bayesian approach. The global optimization methods based on clustering techniques are discussed in a more detailed way. Some other methods using random directions for the search and based on stochastic models are also mentioned.
Reviewer: A.Zilinskas

MSC:
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
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