Convergence of Newton's method for convex best interpolation

In this paper, we consider the problem of finding a convex function which i nterpolates given points and has a minimal L-2 norm of the second derivativ e. This problem reduces to a system of equations involving semismooth funct ions. 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 propos ed by Irvine et al. [17] and settle the question of its convergence. By usi ng a line search strategy, we present a global extension of the Newton meth od considered. The efficiency of the proposed global strategy is confirmed with numerical experiments.