A global Newton method for the nonsmooth vector fields on Riemannian manifolds

DOI10.1007/s10957-021-01881-4zbMath1470.58007OpenAlexW3175569157WikidataQ115382532 ScholiaQ115382532MaRDI QIDQ2046567

Fabrícia R. Oliveira, Fabiana R. de Oliveira

Publication date: 18 August 2021

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-021-01881-4

zbMATH Keywords

regularityglobal convergenceRiemannian manifoldnonmonotone line searchlocally Lipschitz continuous vector fields

Mathematics Subject Classification ID

Derivative-free methods and methods using generalized derivatives (90C56) Newton-type methods (49M15) Nonsmooth analysis (49J52) Global Riemannian geometry, including pinching (53C20) Implicit function theorems; global Newton methods on manifolds (58C15) Real-valued functions on manifolds (58C05)

Related Items

A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the global convergence of the inexact semi-smooth Newton method for absolute value equation
• Nonsmooth optimization techniques on Riemannian manifolds
• Convergence of Newton's method for sections on Riemannian manifolds
• A Levenberg-Marquardt method with approximate projections
• Commutators of flow maps of nonsmooth vector fields
• Convergence of the Newton method and uniqueness of zeros of vector fields on Riemannian manifolds
• A generalized Newton method for absolute value equations
• Newton's method for approximating zeros of vector fields on Riemannian manifolds
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds
• Nonsmooth analysis and Hamilton--Jacobi equations on Riemannian manifolds
• On the Levenberg-Marquardt methods for convex constrained nonlinear equations
• Newton method for finding a singularity of a special class of locally Lipschitz continuous vector fields on Riemannian manifolds
• Damped Newton's method on Riemannian manifolds
• On the superlinear convergence of Newton's method on Riemannian manifolds
• Dini derivative and a characterization for Lipschitz and convex functions on Riemannian manifolds
• An introduction to manifolds. 2nd revised ed.
• An inexact projected LM type algorithm for solving convex constrained nonlinear equations
• A Riemannian Gradient Sampling Algorithm for Nonsmooth Optimization on Manifolds
• The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
• A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
• Nonsmooth analysis on smooth manifolds
• Newton's method on Riemannian manifolds: covariant alpha theory
• Nonmonotone Spectral Projected Gradient Methods on Convex Sets
• The Riemannian Barzilai–Borwein method with nonmonotone line search and the matrix geometric mean computation
• Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds
• Local convergence of Newton's method under a majorant condition in Riemannian manifolds
• Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds
• A Nonmonotone Line Search Technique for Newton’s Method