Inexact Newton Methods and Dennis--Moré Theorems for Nonsmooth Generalized Equations

DOI10.1137/140969476zbMath1321.49044OpenAlexW1972014778MaRDI QIDQ5252506

Asen L. Dontchev, Radek Cibulka, Michel H. Geoffroy

Publication date: 2 June 2015

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/140969476

zbMATH Keywords

set-valued mappingslocal convergenceinexact Newton methodmetric regularityquasi-Newton methodsemismooth functionstrict prederivativeClarke's generalized Jacobiannonsmooth generalized equationsDennis-Moré theorem

Mathematics Subject Classification ID

Nonlinear programming (90C30) Variational inequalities (49J40) Newton-type methods (49M15) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Iterative procedures involving nonlinear operators (47J25) Set-valued operators (47H04) Numerical solutions to equations with nonlinear operators (65J15) Variational and other types of inclusions (47J22)

Related Items (18)

Lipschitz-like mapping and its application to convergence analysis of a variant of Newton's method ⋮ On semiregularity of mappings ⋮ Metrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type Method ⋮ Local convergence analysis of Newton's method for solving strongly regular generalized equations ⋮ Strong metric subregularity of mappings in variational analysis and optimization ⋮ Approximations and generalized Newton methods ⋮ On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property ⋮ Local convergence analysis of an inexact trust-region method for nonsmooth optimization ⋮ Inexact Newton method for non-linear functions with values in a cone ⋮ A general iterative procedure to solve generalized equations with differentiable multifunction ⋮ Newton's method for fully parameterized generalized equations ⋮ Extended Newton-type method for nonlinear functions with values in a cone ⋮ Unnamed Item ⋮ Hölder strong metric subregularity and its applications to convergence analysis of inexact Newton methods ⋮ Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations ⋮ Regularity of Newton's iteration for general parametric variational system ⋮ On Newton's method for solving generalized equations ⋮ Newton's method for solving generalized equations without Lipschitz condition

Cites Work

• Unnamed Item
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• Convergence of inexact Newton methods for generalized equations
• Nonsmooth equations in optimization. Regularity, calculus, methods and applications
• Set-valued approximations and Newton's methods
• The Josephy-Newton method for semismooth generalized equations and semismooth SQP for optimization
• A nonsmooth version of Newton's method
• Infinite dimensional generalized Jacobian: properties and calculus rules
• Generalized Jacobian for functions with infinite dimensional range and domain
• Calculus Without Derivatives
• Newton's Method for Solving Inclusions Using Set-Valued Approximations
• Nonsmooth Equations: Motivation and Algorithms
• Lagrange Multiplier Approach to Variational Problems and Applications
• Optimization and nonsmooth analysis
• Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings
• Inexact Newton Methods
• Solving Nonlinear Equations with Newton's Method
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
• Generalizations of the Dennis--Moré Theorem
• Newton-Type Methods for Optimization and Variational Problems
• Implicit Functions and Solution Mappings

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