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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 12, Pages 2086–2101
DOI: https://doi.org/10.1134/S0044466919120093 (Mi zvmmf10999) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Newton-type method for solving systems of linear equations and inequalities

A. I. Golikovab, Yu. G. Evtushenkoab, I. E. Kaporinab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
b Moscow Institute of Physics and Technology (State University)
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DOI: https://doi.org/10.1134/S0044466919120093
Abstract: A Newton-type method is proposed for numerical minimization of convex piecewise quadratic functions, and its convergence is analyzed. Previously, a similar method was successfully applied to optimization problems arising in mesh generation. It is shown that the method is applicable to computing the projection of a given point onto the set of nonnegative solutions of a system of linear equations and to determining the distance between two convex polyhedra. The performance of the method is tested on a set of problems from the NETLIB repository.
Key words: systems of linear equations and inequalities, regularization, penalty function method, duality, projection of a point, piecewise quadratic function, Newton’s method, preconditioned conjugate gradient method.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00510
This work was supported in part by the Russian Foundation for Basic Research, project no. 17-07-00510.
Received: 27.06.2019
Revised: 27.06.2019
Accepted: 05.08.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 12, Pages 2017–2032
DOI: https://doi.org/10.1134/S0965542519120091
Bibliographic databases:
Document Type: Article
UDC: 7.977
Language: Russian
Citation: A. I. Golikov, Yu. G. Evtushenko, I. E. Kaporin, “Newton-type method for solving systems of linear equations and inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 59:12 (2019), 2086–2101; Comput. Math. Math. Phys., 59:12 (2019), 2017–2032
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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