Convergence of Newton's method for convex best interpolation
Convergence of Newton's method for convex best interpolation
In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal L2 norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. and settle the question of its convergence. By using a line search strategy, we present a global extension of the Newton method considered. The efficiency of the proposed global strategy is confirmed with numerical experiments.
435-456
Dontchev, Asen L.
98d2f989-952e-4c49-a777-2f43cf5ba132
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
January 2001
Dontchev, Asen L.
98d2f989-952e-4c49-a777-2f43cf5ba132
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
Dontchev, Asen L., Qi, Houduo and Qi, Liqun
(2001)
Convergence of Newton's method for convex best interpolation.
Numerische Mathematik, 87 (3), .
(doi:10.1007/PL00005419).
Abstract
In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal L2 norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. and settle the question of its convergence. By using a line search strategy, we present a global extension of the Newton method considered. The efficiency of the proposed global strategy is confirmed with numerical experiments.
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Published date: January 2001
Organisations:
Operational Research
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Local EPrints ID: 29638
URI: http://eprints.soton.ac.uk/id/eprint/29638
PURE UUID: 0e7c721e-7fe6-40d9-8243-d19b5fd482bf
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 03:41
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Author:
Asen L. Dontchev
Author:
Liqun Qi
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