Abstract
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 language | English |
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Pages (from-to) | 435-456 |
Number of pages | 22 |
Journal | Numerische Mathematik |
Volume | 87 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 2001 |
Externally published | Yes |
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics