Computational Optimization and Applications

, Volume 37, Issue 3, pp 409–425

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


DOI: 10.1007/s10589-007-9027-y

Cite this article as:
Qi, H. & Yang, X. Comput Optim Appl (2007) 37: 409. doi:10.1007/s10589-007-9027-y


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.


Convex best interpolation Splines Newton method Regularity Well-posedness Degeneracy 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloonHong Kong, China

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