Regularity and well-posedness of a dual program for convex best C1-spline interpolation


Qi, Hou-Duo and Yang, Xiaoqi.Q. (2007) Regularity and well-posedness of a dual program for convex best C1-spline interpolation Computational Optimization and Applications, 37, pp. 409-425. (doi:10.1007/s10589-007-9027-y).

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Description/Abstract

An efficient approach to computing the convex best C1-spline interpolant to a given set of data is to solve an associated dual program by standard numerical methods (e.g., Newton’s method). We study regularity and well-posedness of the dual program: two important issues that have been not yet well-addressed in the literature. Our regularity results characterize the case when the generalized Hessian of the objective function is positive definite. We also give sufficient conditions for the coerciveness of the objective function. These results together specify conditions when the dual program is well-posed and hence justify why Newton’s method is likely to be successful in practice. Examples are given to illustrate the obtained results.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/s10589-007-9027-y
ISSNs: 0926-6003 (print)
Subjects:
Organisations: Operational Research
ePrint ID: 54537
Date :
Date Event
August 2007Published
Date Deposited: 28 Jul 2008
Last Modified: 16 Apr 2017 17:46
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/54537

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