Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/18956
Title: Regularity and well-posedness of a dual program for convex best C 1-spline interpolation
Authors: Qi, H
Yang, X 
Keywords: Convex best interpolation
Degeneracy
Newton method
Regularity
Splines
Well-posedness
Issue Date: 2007
Publisher: Springer
Source: Computational optimization and applications, 2007, v. 37, no. 3, p. 409-425 How to cite?
Journal: Computational optimization and applications 
Abstract: An efficient approach to computing the convex best C 1-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.
URI: http://hdl.handle.net/10397/18956
ISSN: 0926-6003
EISSN: 1573-2894
DOI: 10.1007/s10589-007-9027-y
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