Ill Posed Variational Problems And Regularization Techniques
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Ill Posed Variational Problems And Regularization Techniques
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Author : Michel Thera
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ill Posed Variational Problems And Regularization Techniques written by Michel Thera and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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.
Ill Posed Variational Problems And Regularization Techniques
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Author : Michel Thera
language : en
Publisher: Springer
Release Date : 1999-11-17
Ill Posed Variational Problems And Regularization Techniques written by Michel Thera and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-17 with Business & Economics categories.
Stable Methods For Iii Posed Variational Problems
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Author : Alexander Kaplan
language : en
Publisher: Wiley-VCH
Release Date : 1994-09-13
Stable Methods For Iii Posed Variational Problems written by Alexander Kaplan and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-13 with Mathematics categories.
Iterative prox-regularization methods for solving ill-posed convex variational problems in Hilbert spaces are subject of this book. A general framework is developed to analyse simultaneously procedures of regularization and successively refined discretization in connection with specific optimization methods for solving the discrete problems. This allows an efficient control of the solution process as a whole. In the first part of the book various methods for treating ill-posed problems are presented, including a study of the regularizing properties of a number of specific optimization algorithms. In the second part, a new class of multi-step methods is introduced which is based on a generalization of the iterative prox-regularization concept. Compared with former methods these new methods permit a more effective use of rough approximations of the infinite dimensional problems and consequently an acceleration of the numerical process. Special versions of these methods are given for ill-posed convex semi-infinite optimization problems and elliptic variational inequalities with weakly coercive operators, including some problems in elasticity theory.
Regularization Algorithms For Ill Posed Problems
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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Regularization Algorithms For Ill Posed Problems written by Anatoly B. Bakushinsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
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
Nonlinear Ill Posed Problems Of Monotone Type
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Author : Yakov Alber
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-02
Nonlinear Ill Posed Problems Of Monotone Type written by Yakov Alber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-02 with Mathematics categories.
Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.
Theory Of Linear Ill Posed Problems And Its Applications
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Author : Valentin K. Ivanov
language : en
Publisher: Walter de Gruyter
Release Date : 2013-02-18
Theory Of Linear Ill Posed Problems And Its Applications written by Valentin K. Ivanov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-18 with Mathematics categories.
This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e. g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces. It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as wall as in ist applications. To reflect these accomplishments the authors included additional material e. g. comments to each chapter and a list of monographs with annotations.
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization
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Author : Jens Flemming
language : en
Publisher: Springer
Release Date : 2018-09-08
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization written by Jens Flemming and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.
Nonlinear Ill Posed Problems
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Author : Andreĭ Nikolaevich Tikhonov
language : en
Publisher:
Release Date : 1998
Nonlinear Ill Posed Problems written by Andreĭ Nikolaevich Tikhonov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Differential equations, Nonlinear categories.
Iterative Regularization Methods For Nonlinear Ill Posed Problems
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Author : Barbara Kaltenbacher
language : en
Publisher: Walter de Gruyter
Release Date : 2008-09-25
Iterative Regularization Methods For Nonlinear Ill Posed Problems written by Barbara Kaltenbacher and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-25 with Mathematics categories.
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Optimal Methods For Ill Posed Problems
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Author : Vitalii P. Tanana
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19
Optimal Methods For Ill Posed Problems written by Vitalii P. Tanana and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems