Local convergence analysis of Newton's method for solving strongly regular generalized equations

DOI10.1016/j.jmaa.2017.09.023zbMath1376.65089arXiv1604.04568OpenAlexW2963179500MaRDI QIDQ1674402

Orizon P. Ferreira, Gilson N. Silva

Publication date: 2 November 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.04568

zbMATH Keywords

convergenceNewton's methodBanach spacestrong regularitymajorant conditiongeneralized nonlinear operator equation

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (7)

Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems ⋮ Extending the Kantorovich's theorem on Newton's method for solving strongly regular generalized equation ⋮ Newton's method with feasible inexact projections for solving constrained generalized equations ⋮ Kantorovich's Theorem on Newton's Method for Solving Strongly Regular Generalized Equation ⋮ On Newton's method for solving generalized equations ⋮ Convergence of quasi-Newton methods for solving constrained generalized equations ⋮ Newton's method for solving generalized equations without Lipschitz condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Newton's method for solving generalized equations: Kantorovich's and Smale's approaches
• Convergence of inexact Newton methods for generalized equations
• Local convergence of Newton's method under majorant condition
• Local convergence analysis of the Gauss-Newton method under a majorant condition
• Convergence analysis of the Gauss-Newton method for convex inclusion and convex-composite optimization problems
• Kantorovich's majorants principle for Newton's method
• Newton's method for generalized equations: a sequential implicit function theorem
• A unifying local convergence result for Newton's method in Riemannian manifolds
• Local convergence of inexact methods under the Hölder condition
• Robinson's implicit function theorem and its extensions
• Smale's point estimate theory for Newton's method on Lie groups
• Local analysis of Newton-type methods for variational inequalities and nonlinear programming
• Nonsmooth equations in optimization. Regularity, calculus, methods and applications
• The convergence ball of Newton's method and the uniqueness ball of equations under Hölder-type continuous derivatives
• A unified convergence theory for Newton-type methods for zeros of nonlinear operators in Banach spaces
• Kantorovich's theorem on Newton's method for solving generalized equations under the majorant condition
• Improved local convergence of Newton's method under weak majorant condition
• Local convergence of quasi-Newton methods under metric regularity
• Extension of Newton's method to nonlinear functions with values in a cone
• Convergence of the Gauss--Newton Method for Convex Composite Optimization under a Majorant Condition
• Metric Regularity of Newton's Iteration
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Strongly Regular Generalized Equations
• Convergence and Complexity of Newton Iteration for Operator Equations
• Convergence of Newton’s method and inverse function theorem in Banach space
• Newton's method on Riemannian manifolds: covariant alpha theory
• Newton-Type Methods for Optimization Problems without Constraint Qualifications
• Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
• Inexact Newton Methods and Dennis--Moré Theorems for Nonsmooth Generalized Equations
• Strong Lipschitz Stability of Stationary Solutions for Nonlinear Programs and Variational Inequalities
• Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle
• Newton's method on Riemannian manifolds: Smale's point estimate theory under the γ-condition
• A Note on the Convergence of Newton’s Method
• Kantorovich's Theorem on Newton's Method for Solving Strongly Regular Generalized Equation

This page was built for publication: Local convergence analysis of Newton's method for solving strongly regular generalized equations