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On the Markov homogeneous optimization method

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Abstract

Estimates of the convergence rate of some homogeneous Markov monotone random search optimization methods are given.

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References

  1. A. A. Zhigljavsky and A. G. Zilinskas, Global Optimization Techniques (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  2. Yu. A. Sushkov, “On a Method for the Organization of Random Search,” in Operations Research and Statistical Modeling, No. 1 (Leningr. Gos. Univ., Leningrad, 1972), pp. 180–186 [in Russian].

    Google Scholar 

  3. A. Sh. Abakarov and Yu. A. Sushkov, “A Statistical Investigation of Random Search,” in Mathematical Modeling: Theory and Applications, No. 2 (Nauchno-Issledovatel’skii Institut Khimii, St. Petersburg Gos. Univ., St. Petersburg, 2002), pp. 70–86 [in Russian].

    Google Scholar 

  4. A. Sh. Abakarov and Yu. A. Sushkov, “Global Optimization: Algorithms and Software,” in Proceedings of the 5th Workshop on Simulation, St. Petersburg, 2005, pp. 1–6.

  5. A. S. Tikhomirov and V. V. Nekrutkin, “Markov Monotone Search for Extrema: Survey of Some Theoretic Results,” in Mathematical Modeling: Theory and Applications, No. 4 (VVM, St. Petersburg, 2004), pp. 3–47 [in Russian].

    Google Scholar 

  6. A. S. Tikhomirov, “Combination of Global and Local Search Methods as Optimization Algorithms,” Zh. Vychisl. Mat. Mat. Fiz. 36, 50–59 (1996).

    MathSciNet  Google Scholar 

  7. F. P. Vasil’ev, Numerical Methods for Solving Extremum Value Problems (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  8. V. G. Karmanov, Mathematical Programming (Fizmatlit, Moscow, 2000) [in Russian].

    Google Scholar 

  9. A. S. Nemirovskii and D. B. Yudin, Complexity of Problems and Efficiency of Optimization Methods (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  10. A. G. Sukharev, Minimax Algorithms in Numerical Analysis (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  11. V. V. Ivanov, “Optimal Minimization Algorithms for Certain Classes of Functions,” Kibernetika, No. 4, 81–94 (1972).

  12. A. S. Tikhomirov, “On the Computational Cost of the Homogeneous Monotone Markov Search for an Extremum,” Available from VINITI, 2004, no. 1452.

  13. A. S. Tikhomirov, “On the Convergence Rate of the Homogeneous Monotone Markov Search for an Extremum,” Available from VINITI, 2004, no. 1934.

  14. A. S. Tikhomirov, “On a Class of Fast Random Search Methods,” in Proceedings of the 5th Workshop on Simulation, St. Petersburg, 2005, pp. 687–690.

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Original Russian Text © A. S. Tikhomirov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 3, pp. 379–394.

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Tikhomirov, A.S. On the Markov homogeneous optimization method. Comput. Math. and Math. Phys. 46, 361–375 (2006). https://doi.org/10.1134/S0965542506030031

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