Modified steepest descent method for nonlinear irregular operator equations
type: Item
instance of: scholarly article
title: Modified steepest descent method for nonlinear irregular operator equations
zbMATH Open document ID: 1334.65099
DOI: 10.1134/S1064562415030187
published in: Doklady Mathematics
publication date: 2015-09-28T00:00:00Z
review text: The author proposes a theoretic two-step iteration method for solving the nonlinear operator equation \(A(u)=f \Longleftrightarrow\) min \(\{\|A(u)-f\|^2: u\in U\}\) in a Hilbert space. The idea is based on transforming the original equation into a regularized equation and then applying a modified steepest descent method to approximate its solution. Although convergence of the proposed method is established, it is unclear how the regularization scheme should be constructed and no numerical example is given.
reviewed by: Zhen Mei
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47J06
zbMATH DE Number: 6485668
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: steepest descent method
zbMATH Keywords: optimization problem
zbMATH Keywords: iteration methods
zbMATH Keywords: regularization
zbMATH Keywords: Hilbert space
zbMATH Keywords: convergence
author: Vladimir Vasin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6485668