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A proximal-Newton method for unconstrained convex optimization in Hilbert spaces

Maicon Marques Alves(maicon.alves***at***ufsc.br)
Benar Fux Svaiter(benar***at***impa.br)

Abstract: We propose and study the iteration-complexity of a proximal-Newton method for finding approximate solutions of the problem of minimizing a twice continuously differentiable convex function on a (possibly infinite dimensional) Hilbert space. We prove global convergence rates for obtaining approximate solutions in terms of function/gradient values. Our main results follow from an iteration-complexity study of an (large-step) inexact proximal point method for solving convex minimization problems.

Keywords: Smooth convex optimization, Proximal-Newton method, Complexity, Proximal point methods

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 10/29/2016
Entry Accepted: 10/29/2016
Entry Last Modified: 10/29/2016

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