Ill Posed Variational Problems And Regularization Techniques
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Ill-posed Variational Problems and Regularization Techniques
Author: Michel Thera
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book presents recent developments in the field of ill-posed variational problems and variational inequalities, covering a large range of theoretical, numerical and practical aspects. The main topics are: - Regularization techniques for equilibrium and fixed point problems, variational inequalities and complementary problems, - Links between approximation, penalization and regularization, - Bundle methods, nonsmooth optimization and regularization, - Error Bounds for regularized optimization problems.
Computational Methods for Inverse Problems
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Regularization Algorithms for Ill-Posed Problems
Author: Anatoly B. Bakushinsky
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2018-02-05
This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems