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Researching the Analogue of the Minimum Error Method in Optimization
Current Issue
Volume 3, 2015
Issue 6 (December)
Pages: 161-164   |   Vol. 3, No. 6, December 2015   |   Follow on         
Paper in PDF Downloads: 65   Since Nov. 3, 2015 Views: 1810   Since Nov. 3, 2015
Natalya S. Samoylenko, Department of Applied Mathematics, Kemerovo State University, Kemerovo, Russia.
Vladimir N. Krutikov, Department of Applied Mathematics, Kemerovo State University, Kemerovo, Russia.
Vladimir V. Meshechkin, Department of Applied Mathematics, Kemerovo State University, Kemerovo, Russia.
The article is devoted to theoretical study of a subgradient step selection method based on the known minimum value of function. It has been shown that this method is an analogue of the minimum error method for solving linear equation systems. The estimate of convergence rate for a sequence of the minimum function values on the current set of method iterations is received.
Subgradient, Convex Function, Linear Algebra, Minimum of Function, Convergence Rate
B. T. Polyak. Minimization of non-smooth functionals. Computational Mathematics and Mathematical Physics, 1969, Vol. 9, No. 3, pp. 507-521.
B. T. Polyak. Introduction to optimization. Moscow, Nauka, 1983.
N. Z. Shore. Methods for minimizing non-differentiable functions and applications. Kiev, Naukova Dumka, 1979.
D. K. Faddeev, V. N. Faddeeva. Computational methods of linear algebra. Moscow, Fizmatgiz, 1960.
V. V. Voevodin, Yu. A. Kuznetsov. Matrices and computations. Moscow, Nauka, 1984.
V. F. Demyanov, L. V. Vasilyev. Non-differentiable optimization. Moscow, Nauka, 1972.
A. S. Nemirovski, D. B. Yudin. Task complexity and efficiency of optimization methods. Moscow, Nauka, 1979.
V. N. Krutikov. Learning methods of unconstrained optimization and applications. Tomsk, TSPU, 2008.
V. N. Krutikov. Relaxation methods for unconstrained optimization, based on the principles of learning. Kemerovo, KemSU, 2004.
V. N. Krutikov, T. V. Petrova. Relaxation method of minimization with space extension in the direction subgradient. Economy and math. methods, 2003, Vol. 39, No. 1, pp. 106-119.
V. N. Krutikov, T. A. Gorskaya. Family of subgradient relaxation methods with two-ranged correction of metric matrices. Economy and math. methods, 2009, Vol. 45, No. 4, pp. 105-120.
V. N. Krutikov, Ya. N. Vershinin. Learning algorithms based on the sequence of the vector orthogonalization. Bulletin of KemSU, 2012, No. 2, pp. 37-42.
V. N. Krutikov, Ya. N. Vershinin. Multistep subgradient method for solving nonsmooth minimization problems of high dimension. TSU Journal of Mathematics and Mechanics, 2014, No. 3, pp. 5-19.
V. N. Krutikov. Subgradient minimization method with descent vectors correction by means of learning relations pairs. Bulletin of KemSU, 2014, No. 1, Vol. 1, pp. 46-54.
V. N. Krutikov. Optimization methods. Kemerovo, KemSU, 2011.
N. S. Samoylenko, V. N. Krutikov, V. V. Meshechkin. On the analogy between the minimum error method and subgradient method. Scientific creativity of young people. Mathematics. Informatics: Proc. of International Conf., Anzhero-Sudzhensk, Russia, 2014.
N. S. Samoylenko, V. N. Krutikov, V. V. Meshechkin. On the assessment of the convergence of subgradient method. Education, science and innovation – the contribution of young researchers: Proc. of International Conf., Kemerovo, Russia, 2014.
N. S. Samoylenko, V. N. Krutikov, V. V. Meshechkin. Research of one variant of subgradient method. Bulletin of KemSU, 2015, No. 2, Vol. 5, pp. 55-5.
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