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On Convergence of a P-Algorithm Based on a Statistical Model of Continuously Differentiable Functions
Authors:James M Calvin  Antanas Zilinskas
Institution:(1) Department of Computer and Information Science, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA;(2) Institute of Mathematics and Informatics, Akademijos str. 4, Vilnius, LT2600, Lithuania
Abstract:This paper is a study of the one-dimensional global optimization problem for continuously differentiable functions. We propose a variant of the so-called P-algorithm, originally proposed for a Wiener process model of an unknown objective function. The original algorithm has proven to be quite effective for global search, though it is not efficient for the local component of the optimization search if the objective function is smooth near the global minimizer. In this paper we construct a P-algorithm for a stochastic model of continuously differentiable functions, namely the once-integrated Wiener process. This process is continuously differentiable, but nowhere does it have a second derivative. We prove convergence properties of the algorithm.
Keywords:Global optimization  Statistical models  Wiener process
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