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Author: Alexander Barvinok
Publisher: American Mathematical Soc.
ISBN: 0821829688
Category : Mathematics
Languages : en
Pages : 378
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Book Description
Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.
Author: Alexander Barvinok
Publisher: American Mathematical Soc.
ISBN: 0821829688
Category : Mathematics
Languages : en
Pages : 378
Get Book Here
Book Description
Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.
Author: Leonard D. Berkovitz
Publisher: John Wiley & Sons
ISBN: 0471461660
Category : Mathematics
Languages : en
Pages : 283
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Book Description
A comprehensive introduction to convexity and optimization inRn This book presents the mathematics of finite dimensionalconstrained optimization problems. It provides a basis for thefurther mathematical study of convexity, of more generaloptimization problems, and of numerical algorithms for the solutionof finite dimensional optimization problems. For readers who do nothave the requisite background in real analysis, the author providesa chapter covering this material. The text features abundantexercises and problems designed to lead the reader to a fundamentalunderstanding of the material. Convexity and Optimization in Rn provides detailed discussionof: * Requisite topics in real analysis * Convex sets * Convex functions * Optimization problems * Convex programming and duality * The simplex method A detailed bibliography is included for further study and an indexoffers quick reference. Suitable as a text for both graduate andundergraduate students in mathematics and engineering, thisaccessible text is written from extensively class-tested notes.
Author: Barry Simon
Publisher: Cambridge University Press
ISBN: 1139497596
Category : Mathematics
Languages : en
Pages : 357
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Book Description
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Author: Lars Hörmander
Publisher: Springer Science & Business Media
ISBN: 0817645853
Category : Mathematics
Languages : en
Pages : 424
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Book Description
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed.
Author: H. G. Eggleston
Publisher: CUP Archive
ISBN: 9780521077347
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This account of convexity includes the basic properties of convex sets in Euclidean space and their applications, the theory of convex functions and an outline of the results of transformations and combinations of convex sets. It will be useful for those concerned with the many applications of convexity in economics, the theory of games, the theory of functions, topology, geometry and the theory of numbers.
Author: Alberto Cambini
Publisher: Springer Science & Business Media
ISBN: 3540708766
Category : Mathematics
Languages : en
Pages : 252
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Book Description
The authors have written a rigorous yet elementary and self-contained book to present, in a unified framework, generalized convex functions. The book also includes numerous exercises and two appendices which list the findings consulted.
Author: M. Rosenfeld
Publisher: Elsevier
ISBN: 0080871984
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.
Author: Mats Andersson
Publisher: Birkhäuser
ISBN: 3034878710
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.
Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 0226199886
Category : Business & Economics
Languages : en
Pages : 175
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Book Description
The caratheodory approach; Infinite-dimensional optimization; Duality theory.
Author: Paul J. Kelly
Publisher:
ISBN: 9780486469805
Category : Convex bodies
Languages : en
Pages : 0
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Book Description
This text assumes no prerequisites, offering an easy-to-read treatment with simple notation and clear, complete proofs. From motivation to definition, its explanations feature concrete examples and theorems. 1979 edition.
