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This article is cited in 5 scientific papers (total in 5 papers)
NUMERICAL METHODS AND THE BASIS FOR THEIR APPLICATION
Correlation and realization of quasi-newton methods of absolute optimization
A. B. Sviridenkoa, G. A. Zelenkovb a FSEI of HPE "Kuban State University" branch in Novorossiysk, 87 Geroev-Desantnikov st., 353922, Russia
b Admiral Ushakov State Maritime University, Novorossisk, 93 Lenin's av., 353922, Russia
Abstract:
Newton and quasi-Newton methods of absolute optimization based on Cholesky factorization with adaptive step and finite difference approximation of the first and the second derivatives. In order to raise effectiveness of the quasi-Newton methods a modified version of Cholesky decomposition of quasi-Newton matrix is suggested. It solves the problem of step scaling while descending, allows approximation by non-quadratic functions, and integration with confidential neighborhood method. An approach to raise Newton methods effectiveness with finite difference approximation of the first and second derivatives is offered. The results of numerical research of algorithm effectiveness are shown.
Keywords:
Newton methods, quasi-Newton methods, Cholesky factorization, step scaling, method of confidence neighborhoods, finite difference approximation, algorithm, numerical research, absolute optimization.
Received: 09.10.2015 Revised: 16.02.2016
Citation:
A. B. Sviridenko, G. A. Zelenkov, “Correlation and realization of quasi-newton methods of absolute optimization”, Computer Research and Modeling, 8:1 (2016), 55–78
Linking options:
https://www.mathnet.ru/eng/crm129 https://www.mathnet.ru/eng/crm/v8/i1/p55
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Abstract page: | 254 | Full-text PDF : | 114 | References: | 25 |
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