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Bayesian stopping rules for multistart global optimization methods. (English) Zbl 0626.90079
The unconstrained global optimization problem of a real-valued multimodal objective function f over a compact set S is considered. To solve this problem one can use local search from each point of a random sample drawn from the uniform distribution over S. If the number of local optima of f is unknown then there is no absolute guarantee that all these local optima have been found in some moment. It is appropriate to treat observed optima as a sample from a multinomial distribution whose cells correspond to the optima of f and the number of cells is equal to the unknown number of the optima of f. The posterior density function of the number of local optima is obtained. Several stopping rules are discussed and test results presented.
Reviewer: E.Tamm

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