Regularization Methods for Ill-Posed Optimal Control Problems PDF Download
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Author: Frank Pörner
Publisher: BoD – Books on Demand
ISBN: 3958260861
Category : Mathematics
Languages : en
Pages : 181
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Book Description
Ill-posed optimization problems appear in a wide range of mathematical applications, and their numerical solution requires the use of appropriate regularization techniques. In order to understand these techniques, a thorough analysis is inevitable. The main subject of this book are quadratic optimal control problems subject to elliptic linear or semi-linear partial differential equations. Depending on the structure of the differential equation, different regularization techniques are employed, and their analysis leads to novel results such as rate of convergence estimates.
Author: Frank Pörner
Publisher: BoD – Books on Demand
ISBN: 3958260861
Category : Mathematics
Languages : en
Pages : 181
Get Book
Book Description
Ill-posed optimization problems appear in a wide range of mathematical applications, and their numerical solution requires the use of appropriate regularization techniques. In order to understand these techniques, a thorough analysis is inevitable. The main subject of this book are quadratic optimal control problems subject to elliptic linear or semi-linear partial differential equations. Depending on the structure of the differential equation, different regularization techniques are employed, and their analysis leads to novel results such as rate of convergence estimates.
Author: Barbara Kaltenbacher
Publisher: Walter de Gruyter
ISBN: 311020827X
Category : Mathematics
Languages : en
Pages : 205
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Book Description
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.
Author:
Publisher: Springer-Verlag
ISBN: 3322930343
Category : Technology & Engineering
Languages : de
Pages : 199
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Book Description
Author: Irwin Yousept
Publisher: Cuvillier Verlag
ISBN: 3867276684
Category :
Languages : en
Pages : 26
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Book Description
Author: Michel Thera
Publisher: Springer Science & Business Media
ISBN: 3642457800
Category : Business & Economics
Languages : en
Pages : 281
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Book Description
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.
Author: Heinz Werner Engl
Publisher: Springer Science & Business Media
ISBN: 9780792361404
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates.
Author: Vladimir Alekseevich Morozov
Publisher: CRC PressI Llc
ISBN: 9780849393112
Category : Mathematics
Languages : en
Pages : 257
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Book Description
Presents current theories and methods for obtaining approximate solutions of basic classes of incorrectly posed problems. The book provides simple conditions of optimality and the optimality of the order of regular methods for solving a wide class of unsteady problems.
Author: Petrov Yuri P.
Publisher: Walter de Gruyter
ISBN: 3110195305
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.
Author: Nupur Goyal
Publisher: CRC Press
ISBN: 1000433153
Category : Technology & Engineering
Languages : en
Pages : 222
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Book Description
Differential Equations in Engineering: Research and Applications describes advanced research in the field of the applications of differential equations in engineering and the sciences, and offers a sound theoretical background, along with case studies. It describes the advances in differential equations in real life for engineers. Along with covering many advanced differential equations and explaining the utility of these equations, the book provides a broad understanding of the use of differential equations to solve and analyze many real-world problems, such as calculating the movement or flow of electricity, the motion of an object to and from, like a pendulum, or explaining thermodynamics concepts by making use of various mathematical tools, techniques, strategies, and methods in applied engineering. This book is written for researchers and academicians, as well as for undergraduate and postgraduate students of engineering.
Author: Semen Ya. Serovaiskii
Publisher: Walter de Gruyter
ISBN: 3110915537
Category : Mathematics
Languages : en
Pages : 185
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Book Description
This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.
