Armijo Newton method for convex best interpolation

Quadratic Convergence of Newton’s Method for Convex Interpolation and Smoothing

In this paper, we prove that Newton’s method for convex best interpolation is locally q-quadratically convergent, giving an answer to a question of Irvine, Marine and Smith [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. A damped Newton-type method is presented which has global q-quadratic convergence. Analogous results are obtained for the convex smoothin...

Block Bfgs Methods

We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also show that Block BFGS is globally convergent to a stationary point when applied to non-convex functions with bounded Hessian, and discuss other modifications...

Finite termination of a dual Newton method for convex best C 1 interpolation and smoothing

A Finite Newton Method for Classification Problems

A fundamental classification problem of data mining and machine learning is that of minimizing a strongly convex, piecewise quadratic function on the n-dimensional real space Rn. We show finite termination of a Newton method to the unique global solution starting from any point in Rn. If the function is well conditioned, then no stepsize is required from the start, and if not, an Armijo stepsiz...

A quadratically convergent Newton method for vector optimization

We propose a Newton method for solving smooth unconstrained vector optimization problems under partial orders induced by general closed convex pointed cones. The method extends the one proposed by Fliege, Graña Drummond and Svaiter for multicriteria, which in turn is an extension of the classical Newton method for scalar optimization. The steplength is chosen by means of an Armijo-like rule, gu...