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

Houduo Qi, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)409-425
Number of pages17
JournalComputational Optimization and Applications
Volume37
Issue number3
DOIs
Publication statusPublished - 1 Jul 2007

Keywords

  • Convex best interpolation
  • Degeneracy
  • Newton method
  • Regularity
  • Splines
  • Well-posedness

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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