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Author: Alexander Kaplan
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 448
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Book Description
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.
Author: Alexander Kaplan
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 448
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Book Description
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.
Author: Alexander Kaplan
Publisher:
ISBN: 9783527400423
Category :
Languages : en
Pages : 438
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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: Nils Langenberg
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832528903
Category : Business & Economics
Languages : en
Pages : 255
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Book Description
Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions may be considered as rather restrictive e.g. in the framework of Nash equilibrium problems. This motivates the development of convergence results under weaker hypotheses which constitute the major subject of the present book. Studied methods include the Bregman-function-based Proximal Point Algorithm (BPPA), Cohen's Auxiliary Problem Principle and an extragradient algorithm.Moreover, this work also contains the first numerical comparison of stopping criteria in the framework of the BPPA. Although such conditions are the subject of theoretical investigations frequently, their numerical effectiveness and a deducible preference were still unknown. This gives rise to the necessity of the presented numerical experiments.
Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 0387747583
Category : Mathematics
Languages : en
Pages : 4646
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Book Description
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Author: Anatoly B. Bakushinsky
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110556383
Category : Mathematics
Languages : en
Pages : 342
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Book Description
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
Author: Yakov Alber
Publisher: Springer Science & Business Media
ISBN: 1402043961
Category : Mathematics
Languages : en
Pages : 422
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Book Description
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.
Author: Peter Gritzmann
Publisher: Springer Science & Business Media
ISBN: 364259073X
Category : Mathematics
Languages : en
Pages : 388
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Book Description
This book presents recent theoretical and practical aspects in the field of optimization and convex analysis. The topics covered in this volume include: - Equilibrium models in economics. - Control theory and semi-infinite programming. - Ill-posed variational problems. - Global optimization. - Variational methods in image restoration. - Nonsmooth optimization. - Duality theory in convex and nonconvex optimization. - Methods for large scale problems.
Author: R.P. Gilbert
Publisher: Springer Science & Business Media
ISBN: 1461302870
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.
Author: Alberto Seeger
Publisher: Springer Science & Business Media
ISBN: 3540282580
Category : Mathematics
Languages : en
Pages : 457
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Book Description
The contributions appearing in this book give an overview of recent research done in optimization and related areas, such as optimal control, calculus of variations, and game theory. They do not only address abstract issues of optimization theory, but are also concerned with the modeling and computer resolution of specific optimization problems arising in industry and applied sciences.
