New versions of Newton method: step-size choice, convergence domain and under-determined equations
From MaRDI portal
Publication:5859005
DOI10.1080/10556788.2019.1669154zbMath1464.90112arXiv1703.07810OpenAlexW2977911200WikidataQ127179329 ScholiaQ127179329MaRDI QIDQ5859005
Publication date: 15 April 2021
Published in: Optimization Methods and Software (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.07810
global convergenceNewton methodnonlinear equationsadaptive algorithmsmetric regularityunder-determined equations
Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Methods of quasi-Newton type (90C53) Implicit function theorems; global Newton methods on manifolds (58C15)
Related Items
Error bound conditions and convergence of optimization methods on smooth and proximally smooth manifolds, Stopping rules for gradient methods for non-convex problems with additive noise in gradient, A short note on an adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations, Some properties of smooth convex functions and Newton's method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On local convexity of quadratic transformations
- On the existence of solutions to nonlinear equations involving singular mappings with non-zero \(p\)-kernel
- A Kantorovich-type convergence analysis for the Gauss-Newton-method
- Analysis and implementation of a dual algorithm for constrained optimization
- Convergence of Newton-like methods for singular operator equations using outer inverses
- Historical developments in convergence analysis for Newton's and Newton-like methods
- A Newton method for systems of \(m\) equations in \(n\) variables.
- Convexity of quadratic transformations and its use in control and optimization
- Sparse solutions of optimal control via Newton method for under-determined systems
- Newton's method, differential equations, and the Lagrangian principle for necessary extremum conditions
- A Newton-Raphson method for the solution of systems of equations
- Newton's method for the solution of systems of equalities and inequalities
- Extension of Newton's method to nonlinear functions with values in a cone
- Newton-Kantorovich method and its global convergence
- Some mapping theorems
- A Gauss-Newton Approach to Solving Generalized Inequalities
- Solving Nonlinear Equations with Newton's Method
- Iterative Solution of Nonlinear Equations in Several Variables
- Variational Analysis of Regular Mappings
- A Rapidly Convergent Descent Method for Minimization
- Implicit Functions and Solution Mappings
- Modified Gauss–Newton scheme with worst case guarantees for global performance
- Gradient methods for solving equations and inequalities
- Convexity of nonlinear image of a small ball with applications to optimization