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On Convergence of a P-Algorithm Based on a Statistical Model of Continuously Differentiable Functions

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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.

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References

  • Archetti, F. and Betrò, B. (1979), A probabilistic algorithm for global optimization. Calcolo, 16, 335-343.

    Google Scholar 

  • Calvin, J. (1999), Convergence rate of the P-algorithm for optimization of continuous functions. In Pardalos, P.M. (ed.), Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, Kluwer Academic Publishers, Boston.

    Google Scholar 

  • Calvin, J. and Žilinskas, A. (1999), On convergence of the P-algorithm for one dimensional global optimization of smooth functions. Journal of Optimization Theory and Application 102(3): 479-495.

    Google Scholar 

  • Kushner, H. (1964), A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Journal of Basic Engineering, 86: 97-106.

    Google Scholar 

  • Locatelli, M. (1997), Bayesian algorithms for one-dimensional global optimization. Journal of Global Optimization, 10: 57-76.

    Google Scholar 

  • Locatelli, M. and Schoen, F. (1995), An adaptive stochastic global optimization algorithm for one-dimensional functions. Annals of Operations Research 58: 263-278.

    Google Scholar 

  • Novak, E. and Ritter, K. (1993), Some complexity results for zero finding for univariate functions. Journal of Complexity, 9: 15-40.

    Google Scholar 

  • Ritter, K. (1990), Approximation and optimization on the Wiener space. Journal of Complexity, 6: 337-364.

    Google Scholar 

  • Törn, A. and Žilinskas, A. (1989). Global Optimization. Springer-Verlag, Berlin.

    Google Scholar 

  • Žilinskas, A. (1985), Axiomatic characterization of global optimization algorithm and investigation of its search strategy. OR Letters 4: 35-39.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer and Information Science, New Jersey Institute of Technology, Newark, NJ, 07102-1982, USA

    James M. Calvin

  2. Institute of Mathematics and Informatics, Akademijos str. 4, Vilnius, LT2600, Lithuania

    Antanas Zilinskas

Authors
  1. James M. Calvin
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  2. Antanas Zilinskas
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Calvin, J.M., Zilinskas, A. On Convergence of a P-Algorithm Based on a Statistical Model of Continuously Differentiable Functions. Journal of Global Optimization 19, 229–245 (2001). https://doi.org/10.1023/A:1011207622164

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  • DOI: https://doi.org/10.1023/A:1011207622164

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