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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)
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.
Received: 27.06.2019 Revised: 27.06.2019 Accepted: 05.08.2019
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10999 https://www.mathnet.ru/eng/zvmmf/v59/i12/p2086
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Abstract page: | 115 | References: | 12 |
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