Convex Variational Problems
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Convex Variational Problems
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Author : Michael Bildhauer
language : en
Publisher: Springer
Release Date : 2003-07-03
Convex Variational Problems written by Michael Bildhauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Mathematics categories.
The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.
Convex Analysis And Variational Problems
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Author : Ivar Ekeland
language : en
Publisher: SIAM
Release Date : 1999-12-01
Convex Analysis And Variational Problems written by Ivar Ekeland and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.
This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
One Dimensional Variational Problems
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Author : Giuseppe Buttazzo
language : en
Publisher: Oxford University Press
Release Date : 1998
One Dimensional Variational Problems written by Giuseppe Buttazzo and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
The Effect Of A Singular Perturbation To A 1 D Non Convex Variational Problem
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Author : Markus Lilli
language : en
Publisher: Logos Verlag Berlin
Release Date : 2005
The Effect Of A Singular Perturbation To A 1 D Non Convex Variational Problem written by Markus Lilli and has been published by Logos Verlag Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Nichtkonvexes Variationsproblem - Singuläre Störung - Euler-Lagrange-Gleichung categories.
Nonconvex variational problems are of importance in modeling problems of microstructures and elasticity. In this book, we consider a $1$-d nonconvex problem and we prove existence of solutions of the corresponding non-elliptic Euler-Lagrange equation by considering the Euler-Lagrange equation of the singular perturbed variational problem and passing to the limit. Under general assumptions on the potential we prove existence of Young-measure solutions. More restrictive conditions on the potential yield classical solutions via a topological method. The singular perturbed problem, which is also of interest for physicists due to the higher gradient surface-energy, is discussed in big detail.
Noncoercive Variational Problems And Related Results
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Author : Daniel Goeleven
language : en
Publisher: CRC Press
Release Date : 1996-10-10
Noncoercive Variational Problems And Related Results written by Daniel Goeleven and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-10 with Mathematics categories.
In establishing a general theory of the existence of solutions for noncoercive variational problems and constrained problems formulated as variational inequalities or hemivariational inequalities, this Research Note illustrates recent mathematical approaches and results with various examples from mathematics and mechanics. The book unifies ideas for the treatment of various noncoercive problems and provides previously unpublished results for variational inequalities and hemivariational inequalities. The author points out important applications in mechanics and their mathfematical tratment using recession tools. This book will be of particular interest to researchers in pure and aplied mathematics and mechanics.
Convex Analysis And Variational Problems
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Author : Ivar Ekeland
language : en
Publisher: SIAM
Release Date : 1999-12-01
Convex Analysis And Variational Problems written by Ivar Ekeland and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.
No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
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.
Lagrange Multiplier Approach To Variational Problems And Applications
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Author : Kazufumi Ito
language : en
Publisher: SIAM
Release Date : 2008-01-01
Lagrange Multiplier Approach To Variational Problems And Applications written by Kazufumi Ito and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.
Nonlinear Analysis And Variational Problems
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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-20
Nonlinear Analysis And Variational Problems written by Panos M. Pardalos 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 2009-10-20 with Business & Economics categories.
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
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.