Some theoretical aspects of Newton's method for constrained best interpolation
Some theoretical aspects of Newton's method for constrained best interpolation
The paper contains new results as well as surveys on recent developments on the constrained best interpolation problem, and in particular on the convex best interpolation problem. Issues addressed include theoretical reduction of the problem to a system of nonsmooth equations, nonsmooth analysis of those equations and development of Newton's method, convergence analysis and globalization.
We frequently use the convex best interpolation to illustrate the seemingly complex theory. Important techniques such as splitting are introduced and interesting links between approaches from approximation and optimization are also established. Open problems related to polyhedral constraints and strips may be tackled by the tools introduced and developed in this paper.
9780387267
253-270
Cambridge University Press
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
2005
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Houduo
(2005)
Some theoretical aspects of Newton's method for constrained best interpolation.
In,
Jeyakumar, Vaithilingam and Rubinov, Alexander
(eds.)
Continuous Optimization: Current Trends and Modern Applications.
Cambridge, UK, New York, USA.
Cambridge University Press, .
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Abstract
The paper contains new results as well as surveys on recent developments on the constrained best interpolation problem, and in particular on the convex best interpolation problem. Issues addressed include theoretical reduction of the problem to a system of nonsmooth equations, nonsmooth analysis of those equations and development of Newton's method, convergence analysis and globalization.
We frequently use the convex best interpolation to illustrate the seemingly complex theory. Important techniques such as splitting are introduced and interesting links between approaches from approximation and optimization are also established. Open problems related to polyhedral constraints and strips may be tackled by the tools introduced and developed in this paper.
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Published date: 2005
Organisations:
Operational Research
Identifiers
Local EPrints ID: 29651
URI: http://eprints.soton.ac.uk/id/eprint/29651
ISBN: 9780387267
PURE UUID: 9d9a5565-bc6b-4b37-8e42-b9be710a2e89
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Date deposited: 15 May 2006
Last modified: 12 Dec 2021 03:28
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Contributors
Editor:
Vaithilingam Jeyakumar
Editor:
Alexander Rubinov
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