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An orthogonal descent algorithm to find the zero of a convex function, unsolvability test, and rate of convergence

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The paper is the first in a series of articles on the orthogonal descent method. The unsolvability test is considered and the rate of convergence is determined for the algorithm that finds a point with a prescribed value of a convex function.

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  1. 1.

    M. B. Shchepakin, “On properties of sum displacement directions,” Kibernetika, No. 1, 135–136 (1978).

  2. 2.

    F. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York (1983).

  3. 3.

    B. T. Polyak, An Introduction to Optimization [in Russian], Nauka, Moscow (1983).

  4. 4.

    B. T. Polyak, “Minimization of nonsmooth functionals,” Zh. Vychisl. Mat. Mat. Fiz.,9, No. 3, 507–521 (1969).

  5. 5.

    L. G. Gurin, B. T. Polyak, and É. V. Raik, “Projection methods to find a common point of convex sets,” Zh. Vychisl. Mat. Mat. Fiz.,7, No. 6, 1211–1228 (1967).

  6. 6.

    M. B. Shchepakin, “A Fejér method of nondifferentiable optimization,” Dokl. Akad. Nauk SSSR,30, No. 6, 135–136 (1988).

  7. 7.

    M. B. Shchepakin, “On the orthogonal descent method,” Kibernetika, No. 1, 58–62 (1987).

  8. 8.

    M. B. Shchepakin, “On an inconsistency test for a system of convex inequalities for a class of Fejér approximations,” Kibernetika, No. 2, 124 (1985).

  9. 9.

    L. G. Khachiyan, “Polynomial algorithms in linear programming,” Zh. Vychisl. Mat. Mat. Fiz.,20, No. 1, 51–68 (1980).

  10. 10.

    Z. Drezner, “The nested ball principle for the relaxation method,” Oper. Res.,31, No. 3, 587–590 (1983).

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Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 87–96, September–October, 1992.

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Shchepakin, M.B. An orthogonal descent algorithm to find the zero of a convex function, unsolvability test, and rate of convergence. Cybern Syst Anal 28, 727–734 (1992). https://doi.org/10.1007/BF01131851

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  • Operating System
  • Artificial Intelligence
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  • Convex Function
  • Descent Method