Fundamentals Of Convex Analysis
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| Author | : Jean-Baptiste Hiriart-Urruty |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642564682 |
Download Fundamentals of Convex Analysis Book in PDF, Epub and Kindle
This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of bot volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched, making it an excellent choice for the purpose of learning and teaching.
| Author | : Jean-Baptiste Hiriart-Urruty |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 278 |
| Release | : 2004-04-21 |
| Genre | : Computers |
| ISBN | : 9783540422051 |
Download Fundamentals of Convex Analysis Book in PDF, Epub and Kindle
This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of bot volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched, making it an excellent choice for the purpose of learning and teaching.
| Author | : Jean-Baptiste Hiriart-Urruty |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 432 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662027968 |
Download Convex Analysis and Minimization Algorithms I Book in PDF, Epub and Kindle
Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.
| Author | : Chong-Yung Chi |
| Publisher | : CRC Press |
| Total Pages | : 294 |
| Release | : 2017-01-24 |
| Genre | : Technology & Engineering |
| ISBN | : 1315349809 |
Download Convex Optimization for Signal Processing and Communications Book in PDF, Epub and Kindle
Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications provides fundamental background knowledge of convex optimization, while striking a balance between mathematical theory and applications in signal processing and communications. In addition to comprehensive proofs and perspective interpretations for core convex optimization theory, this book also provides many insightful figures, remarks, illustrative examples, and guided journeys from theory to cutting-edge research explorations, for efficient and in-depth learning, especially for engineering students and professionals. With the powerful convex optimization theory and tools, this book provides you with a new degree of freedom and the capability of solving challenging real-world scientific and engineering problems.
| Author | : Ralph Tyrell Rockafellar |
| Publisher | : Princeton University Press |
| Total Pages | : 470 |
| Release | : 2015-04-29 |
| Genre | : Mathematics |
| ISBN | : 1400873177 |
Download Convex Analysis Book in PDF, Epub and Kindle
Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions. This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.
| Author | : Andrew J. Kurdila |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2006-03-30 |
| Genre | : Science |
| ISBN | : 3764373571 |
Download Convex Functional Analysis Book in PDF, Epub and Kindle
This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
| Author | : M.J. Panik |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 313 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 940158124X |
Download Fundamentals of Convex Analysis Book in PDF, Epub and Kindle
Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and complementary slackness; extreme points and directions; resolution and representation of polyhedra; simplicial topology; and fixed point theorems, among others. A strength of this work is how these topics are developed in a fully integrated fashion.
| Author | : Georgii G. Magaril-Ilʹyaev |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 196 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821889640 |
Download Convex Analysis Book in PDF, Epub and Kindle
This book is an introduction to convex analysis and some of its applications. It starts with basis theory, which is explained within the framework of finite-dimensional spaces. The only prerequisites are basic analysis and simple geometry. The second chapter presents some applications of convex analysis, including problems of linear programming, geometry, and approximation. Special attention is paid to applications of convex analysis to Kolmogorov-type inequalities for derivatives of functions is one variable. Chapter 3 collects some results on geometry and convex analysis in infinite-dimensional spaces. A comprehensive introduction written "for beginners" illustrates the fundamentals of convex analysis in finite-dimensional spaces. The book can be used for an advanced undergraduate or graduate level course on convex analysis and its applications. It is also suitable for independent study of this extremely important area of mathematics.
| Author | : Dimitri Bertsekas |
| Publisher | : Athena Scientific |
| Total Pages | : 576 |
| Release | : 2015-02-01 |
| Genre | : Mathematics |
| ISBN | : 1886529280 |
Download Convex Optimization Algorithms Book in PDF, Epub and Kindle
This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.
| Author | : Erhan Çınlar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 164 |
| Release | : 2013-01-04 |
| Genre | : Mathematics |
| ISBN | : 1461452570 |
Download Real and Convex Analysis Book in PDF, Epub and Kindle
This book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as part of the curriculum in a graduate program. The book is built around metric spaces. In the first three chapters, the authors lay the foundational material and cover the all-important “four-C’s”: convergence, completeness, compactness, and continuity. In subsequent chapters, the basic tools of analysis are used to give brief introductions to differential and integral equations, convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. It lays the groundwork for the needs of classical fields as well as the important new fields of optimization and probability theory.
