Convergence of Newton's method for convex best interpolation

Asen L. Dontchev, Houduo Qi, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)


In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal L2norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. [17] and settle the question of its convergence. By using a line search strategy, we present a global extension of the Newton method considered. The efficiency of the proposed global strategy is confirmed with numerical experiments.
Original languageEnglish
Pages (from-to)435-456
Number of pages22
JournalNumerische Mathematik
Issue number3
Publication statusPublished - 1 Jan 2001
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this