Functional Analysis and Applied Optimization in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functional Analysis and Applied Optimization in Banach Spaces write by Fabio Botelho. This book was released on 2014-06-12. Functional Analysis and Applied Optimization in Banach Spaces available 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.
Convexity and Optimization in Banach Spaces
Convexity and Optimization in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convexity and Optimization in Banach Spaces write by Viorel Barbu. This book was released on 2012-01-03. Convexity and Optimization in Banach Spaces available 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.
Optimization in Function Spaces with Stability Considerations in Orlicz Spaces
Optimization in Function Spaces with Stability Considerations in Orlicz Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimization in Function Spaces with Stability Considerations in Orlicz Spaces write by Peter Kosmol. This book was released on 2011. Optimization in Function Spaces with Stability Considerations in Orlicz Spaces available 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
Optimization on Metric and Normed Spaces
Optimization on Metric and Normed Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimization on Metric and Normed Spaces write by Alexander J. Zaslavski. This book was released on 2010-08-05. Optimization on Metric and Normed Spaces available in PDF, EPUB and Kindle. "Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.
Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering write by Fabio Silva Botelho. This book was released on 2020-11-02. Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering available in PDF, EPUB and Kindle. The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
