5 papers
An Adaptive Proximal Point Method for Nonsmooth and Nonconvex Optimization on Hadamard Manifolds
Vitaliano S. Amaral, Marcio Antônio de A. Bortoloti, Jurandir O. Lopes +1
This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining…
Local convergence of an inexact proximal algorithm for weakly convex functions
Valdines Leite de Sousa Junior, Lucas Vidal de Meireles, Samara Costa Lima +1
Since introduced by Martinet and Rockafellar, the proximal point algorithm was generalized in many fruitful directions. More recently, in 2002, Pennanen studied the proximal point…
Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds
Mauricio S. Louzeiro, Gilson N. Silva, Jinyun Yuan +1
The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Unde…
Local convergence of Newton's method for solving generalized equations with monotone operator
Gilson N. Silva
In this paper we study Newton's method for solving the generalized equation in Hilbert spaces, where is a Fréchet differentiable function and is set-valued…
On the Kantorovich's theorem for Newton's method for solving generalized equations under the majorant condition
Gilson N. Silva
In this paper we consider a version of the Kantorovich's theorem for solving the generalized equation , where is a Fréchet derivative function and is a set-…