Genericity In Nonlinear Analysis
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Genericity In Nonlinear Analysis
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Author : Simeon Reich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Genericity In Nonlinear Analysis written by Simeon Reich 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 2013-11-21 with Mathematics categories.
This book presents an extensive collection of state-of-the-art results and references in nonlinear functional analysis demonstrating how the generic approach proves to be very useful in solving many interesting and important problems. Nonlinear analysis plays an ever-increasing role in theoretical and applied mathematics, as well as in many other areas of science such as engineering, statistics, computer science, economics, finance, and medicine. The text may be used as supplementary material for graduate courses in nonlinear functional analysis, optimization theory and approximation theory, and is a treasure trove for instructors, researchers, and practitioners in mathematics and in the mathematical sciences. Each chapter is self-contained; proofs are solid and carefully communicated. Genericity in Nonlinear Analysis is the first book to systematically present the generic approach to nonlinear analysis. Topics presented include convergence analysis of powers and infinite products via the Baire Category Theorem, fixed point theory of both single- and set-valued mappings, best approximation problems, discrete and continuous descent methods for minimization in a general Banach space, and the structure of minimal energy configurations with rational numbers in the Aubry–Mather theory.
Nonlinear Analysis Of Structures 1997
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Author : Muthukrishnan Sathyamoorthy
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Nonlinear Analysis Of Structures 1997 written by Muthukrishnan Sathyamoorthy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
Nonlinear Analysis of Structures presents a complete evaluation of the nonlinear static and dynamic behavior of beams, rods, plates, trusses, frames, mechanisms, stiffened structures, sandwich plates, and shells. These elements are important components in a wide variety of structures and vehicles such as spacecraft and missiles, underwater vessels and structures, and modern housing. Today's engineers and designers must understand these elements and their behavior when they are subjected to various types of loads. Coverage includes the various types of nonlinearities, stress-strain relations and the development of nonlinear governing equations derived from nonlinear elastic theory. This complete guide includes both mathematical treatment and real-world applications, with a wealth of problems and examples to support the text. Special topics include a useful and informative chapter on nonlinear analysis of composite structures, and another on recent developments in symbolic computation. Designed for both self-study and classroom instruction, Nonlinear Analysis of Structures is also an authoritative reference for practicing engineers and scientists. One of the world's leaders in the study of nonlinear structural analysis, Professor Sathyamoorthy has made significant research contributions to the field of nonlinear mechanics for twenty-seven years. His foremost contribution to date has been the development of a unique transverse shear deformation theory for plates undergoing large amplitude vibrations and the examination of multiple mode solutions for plates. In addition to his notable research, Professor Sathyamoorthy has also developed and taught courses in the field at universities in India, Canada, and the United States.
Genericity In Polynomial Optimization
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Author : Tien Son Pham
language : en
Publisher: World Scientific
Release Date : 2016-12-22
Genericity In Polynomial Optimization written by Tien Son Pham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Mathematics categories.
In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.Explanations focus on critical points and tangencies of polynomial optimization, Hölderian error bounds for polynomial systems, Frank-Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.
The Projected Subgradient Algorithm In Convex Optimization
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2020-11-25
The Projected Subgradient Algorithm In Convex Optimization written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.
This focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general. The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization. The subgradient projection algorithm is one of the most important tools in optimization theory and its applications. An optimization problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different. This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this. In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning.
Approximate Solutions Of Common Fixed Point Problems
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2016-06-30
Approximate Solutions Of Common Fixed Point Problems written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Mathematics categories.
This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space“/p> · dynamic string-averaging version of the proximal algorithm · common fixed point problems in metric spaces · common fixed point problems in the spaces with distances of the Bregman type · a proximal algorithm for finding a common zero of a family of maximal monotone operators · subgradient projections algorithms for convex feasibility problems in Hilbert spaces
Complex Analysis And Dynamical Systems Vii
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Author : Mark L. Agranovsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2017
Complex Analysis And Dynamical Systems Vii written by Mark L. Agranovsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
A co-publication of the AMS and Bar-Ilan University This volume contains the proceedings of the Seventh International Conference on Complex Analysis and Dynamical Systems, held from May 10–15, 2015, in Nahariya, Israel. The papers in this volume range over a wide variety of topics in the interaction between various branches of mathematical analysis. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, geometry, harmonic analysis, and partial differential equations, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis.
Communications On Applied Nonlinear Analysis
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Author :
language : en
Publisher:
Release Date : 2003
Communications On Applied Nonlinear Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Nonlinear functional analysis categories.
The Generic Chaining
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Author : Michel Talagrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-17
The Generic Chaining written by Michel Talagrand 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 2005-03-17 with Mathematics categories.
The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.
Approximate Fixed Points Of Nonexpansive Mappings
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2024-09-25
Approximate Fixed Points Of Nonexpansive Mappings written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-25 with Mathematics categories.
Fixed point theory of nonlinear operators has been a rapidly growing area of research and plays an important role in the study of variational inequalities, monotone operators, feasibility problems, and optimization theory, to name just several. This book discusses iteration processes associated with a given nonlinear mapping which generate its approximate fixed point and in some cases converge to a fixed point of the mapping. Various classes of nonlinear single-valued and set-valued mappings are considered along with iteration processes under the presence of computational errors. Of particular interest to mathematicians working in fixed point theory and nonlinear analysis, the added value for the reader are the solutions presented to a number of difficult problems in the fixed point theory which have important applications.
Nasa Workshop On Computational Structural Mechanics 1987 Part 2
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Author :
language : en
Publisher:
Release Date : 1989
Nasa Workshop On Computational Structural Mechanics 1987 Part 2 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.