On the Convergence of the P-Algorithm for One-Dimensional Global Optimization of Smooth Functions

J. Calvin and A. Žilinskas
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J. Calvin: New Jersey Institute of Technology
A. Žilinskas: Institute of Mathematics and Informatics

Journal of Optimization Theory and Applications, 1999, vol. 102, issue 3, No 1, 479-495

Abstract: Abstract The Wiener process is a widely used statistical model for stochastic global optimization. One of the first optimization algorithms based on a statistical model, the so-called P-algorithm, was based on the Wiener process. Despite many advantages, this process does not give a realistic model for many optimization problems, particularly from the point of view of local behavior. In the present paper, a version of the P-algorithm is constructed based on a stochastic process with smooth sampling functions. It is shown that, in such a case, the algorithm has a better convergence rate than in the case of the Wiener process. A similar convergence rate is proved for a combination of the Wiener model-based P-algorithm with quadratic fit-based local search.

Keywords: Global optimization; Gaussian processes (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1022677121193

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