Newton's Method for Solving Inclusions Using Set-Valued Approximations

DOI10.1137/130926730zbMath1356.49041OpenAlexW1982110324MaRDI QIDQ2954381

Samir Adly, Huynh Van Ngai, Radek Cibulka

Publication date: 13 January 2017

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

Full work available at URL: https://doi.org/10.1137/130926730

zbMATH Keywords

Newton's methodmetric regularitygeneralized equationproximal point methodforward-backward splittingsemismooth functionset-valued approximations

Mathematics Subject Classification ID

Nonlinear programming (90C30) Newton-type methods (49M15) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53)

Related Items

Newton's method for solving generalized equations: Kantorovich's and Smale's approaches ⋮ 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 ⋮ Stability of metric regularity with set-valued perturbations and application to Newton's method for solving generalized equations ⋮ Approximations and generalized Newton methods ⋮ An improved stability result on the metric regularity under Lipschitz set-valued perturbations ⋮ Kantorovich-type results for generalized equations with applications ⋮ Radius theorems for subregularity in infinite dimensions ⋮ The radius of metric regularity revisited ⋮ Polyhedral optimization of discrete and partial differential inclusions of parabolic type ⋮ Unnamed Item ⋮ Inexact Newton method for non-linear functions with values in a cone ⋮ Existence and continuity of solution trajectories of generalized equations with application in electronics ⋮ A general iterative procedure to solve generalized equations with differentiable multifunction ⋮ Newton's method for fully parameterized generalized equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Hölder strong metric subregularity and its applications to convergence analysis of inexact Newton methods ⋮ Regularity of implicit solution mapping to parametric generalized equation ⋮ Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations ⋮ Preconditioned proximal point methods and notions of partial subregularity ⋮ Regularity of Newton's iteration for general parametric variational system ⋮ Nonsmooth Kantorovich-Newton methods: hypotheses and auxiliary problems ⋮ Metric regularity relative to a cone ⋮ Inexact Newton Methods and Dennis--Moré Theorems for Nonsmooth Generalized Equations ⋮ Convergence of quasi-Newton methods for solving constrained generalized equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Newton's method for solving generalized equations without Lipschitz condition

This page was built for publication: Newton's Method for Solving Inclusions Using Set-Valued Approximations