A proximal-Newton method for unconstrained convex optimization in Hilbert spaces. (2nd January 2018)

• Record Type: Journal Article
• Authors: Alves, M. Marques; Svaiter, Benar F.
• Is Part Of: Optimization. Volume 67:Number 1(2018)
• Page Start: 67
• Page End: 82
• Publication Date: 2018-01-02
• Subjects: Smooth convex optimization -- proximal-Newton method -- complexity -- proximal point methods; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1389942
• Languages: English
• ISSNs: 0233-1934

Abstract

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.