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

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

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the first author was partially supported by CNPq [grant number 406250/2013-8], [grant number 306317/2014-1], [grant number 405214/2016-2]. The work of the second author was partially supported by CNPq [grant number 306247/2015-1]; FAPERJ [grant number E-26/201-584/2014].