Optimization In Function Spaces PDF Download
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Author | : Peter Kosmol |
Publisher | : Walter de Gruyter |
Total Pages | : 405 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 3110250209 |
Download Optimization in Function Spaces with Stability Considerations in Orlicz Spaces Book in PDF, ePub and Kindle
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
Author | : Amol Sasane |
Publisher | : Courier Dover Publications |
Total Pages | : 260 |
Release | : 2016-03-15 |
Genre | : Mathematics |
ISBN | : 0486789454 |
Download Optimization in Function Spaces Book in PDF, ePub and Kindle
Classroom-tested at the London School of Economics, this original, highly readable text offers numerous examples and exercises as well as detailed solutions. Prerequisites are multivariable calculus and basic linear algebra. 2015 edition.
Author | : Peter Kosmol |
Publisher | : Walter de Gruyter |
Total Pages | : 405 |
Release | : 2011-02-28 |
Genre | : Mathematics |
ISBN | : 3110250217 |
Download Optimization in Function Spaces Book in PDF, ePub and Kindle
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
Author | : Fabio Botelho |
Publisher | : Springer |
Total Pages | : 584 |
Release | : 2014-06-12 |
Genre | : Mathematics |
ISBN | : 3319060740 |
Download Functional Analysis and Applied Optimization in Banach Spaces Book in PDF, ePub and Kindle
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Author | : Viorel Barbu |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2012-01-03 |
Genre | : Mathematics |
ISBN | : 940072246X |
Download Convexity and Optimization in Banach Spaces Book in PDF, ePub and Kindle
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
Author | : Michael Ulbrich |
Publisher | : SIAM |
Total Pages | : 315 |
Release | : 2011-07-28 |
Genre | : Mathematics |
ISBN | : 1611970687 |
Download Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book in PDF, ePub and Kindle
A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.
Author | : David G. Luenberger |
Publisher | : John Wiley & Sons |
Total Pages | : 348 |
Release | : 1997-01-23 |
Genre | : Technology & Engineering |
ISBN | : 9780471181170 |
Download Optimization by Vector Space Methods Book in PDF, ePub and Kindle
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Author | : Yutaka Yamamoto |
Publisher | : SIAM |
Total Pages | : 270 |
Release | : 2012-10-31 |
Genre | : Mathematics |
ISBN | : 1611972302 |
Download From Vector Spaces to Function Spaces Book in PDF, ePub and Kindle
A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.
Author | : Juan Peypouquet |
Publisher | : Springer |
Total Pages | : 132 |
Release | : 2015-03-18 |
Genre | : Mathematics |
ISBN | : 3319137107 |
Download Convex Optimization in Normed Spaces Book in PDF, ePub and Kindle
This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.
Author | : Michael Ulbrich |
Publisher | : SIAM |
Total Pages | : 322 |
Release | : 2011-01-01 |
Genre | : Constrained optimization |
ISBN | : 9781611970692 |
Download Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book in PDF, ePub and Kindle
Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.