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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.
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].