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Convexity
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Book Synopsis A Course in Convexity by : Alexander Barvinok
Download or read book A Course in Convexity written by Alexander Barvinok and published by American Mathematical Soc.. This book was released on 2002-11-19 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convexity and Optimization in Rn by : Leonard D. Berkovitz
Download or read book Convexity and Optimization in Rn written by Leonard D. Berkovitz and published by John Wiley & Sons. This book was released on 2003-04-14 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Convexity written by H. G. Eggleston and published by CUP Archive. This book was released on 1958 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Convexity written by Barry Simon and published by Cambridge University Press. This book was released on 2011-05-19 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Notions of Convexity by : Lars Hörmander
Download or read book Notions of Convexity written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry and Convexity by : Paul J. Kelly
Download or read book Geometry and Convexity written by Paul J. Kelly and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Convexity and Optimization by : Alberto Cambini
Download or read book Generalized Convexity and Optimization written by Alberto Cambini and published by Springer Science & Business Media. This book was released on 2008-10-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convexity and Well-Posed Problems by : Roberto Lucchetti
Download or read book Convexity and Well-Posed Problems written by Roberto Lucchetti and published by Springer Science & Business Media. This book was released on 2006-02-02 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de?ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions, i. e. , functions taking possibly the values?? and +?. The reason for considering the value +? is the powerful device of including the constraint set of a constrained minimum problem into the objective function itself (by rede?ning it as +? outside the constraint set). Except for trivial cases, the minimum value must be taken at a point where the function is not +?, hence at a point in the constraint set. And the value ?? is allowed because useful operations, such as the inf-convolution, can give rise to functions valued?? even when the primitive objects are real valued. Observe that de?ning the objective function to be +? outside the closed constraint set preserves lower semicontinuity, which is the pivotal and mi- mal continuity assumption one needs when dealing with minimum problems. Variational calculus is usually based on derivatives.
Book Synopsis Convexity and Graph Theory by : M. Rosenfeld
Download or read book Convexity and Graph Theory written by M. Rosenfeld and published by Elsevier. This book was released on 1984-01-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convexity and Optimization in Finite Dimensions I by : Josef Stoer
Download or read book Convexity and Optimization in Finite Dimensions I written by Josef Stoer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back ground for the arithmetic of convex optimization to be treated in a sub sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.
Book Synopsis Polynomial Convexity by : Edgar Lee Stout
Download or read book Polynomial Convexity written by Edgar Lee Stout and published by Springer Science & Business Media. This book was released on 2007-05-03 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph details polynomially convex sets. It presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. Coverage examines in considerable detail questions of uniform approximation for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. The book also discusses important applications and motivates the reader with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.
Book Synopsis Complex Convexity and Analytic Functionals by : Mats Andersson
Download or read book Complex Convexity and Analytic Functionals written by Mats Andersson and published by Birkhäuser. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convexity and Optimization in Banach Spaces by : Viorel Barbu
Download or read book Convexity and Optimization in Banach Spaces written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Duration, Convexity, and Other Bond Risk Measures by : Frank J. Fabozzi
Download or read book Duration, Convexity, and Other Bond Risk Measures written by Frank J. Fabozzi and published by John Wiley & Sons. This book was released on 1999-05-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Duration, Convexity and other Bond Risk Measures offers the most comprehensive coverage of bond risk measures available. Financial expert Frank Fabozzi walks you through every aspect of bond risk measures from the price volatility characteristics of option-free bonds and bonds with embedded options to the proper method for calculating duration and convexity. Whether you're a novice trader or experienced money manager, if you need to understand the interest rate risk of a portfolio Duration, Convexity and other Bond Risk Measures is the only book you'll need.
Book Synopsis Strict Convexity and Complex Strict Convexity by : Vasile I. Istratescu
Download or read book Strict Convexity and Complex Strict Convexity written by Vasile I. Istratescu and published by Routledge. This book was released on 2017-10-19 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important work provides a comprehensive overview of the properties of Banachspaces related to strict convexity and a survey of significant applications-uniting a wealthof information previously scattered throughout the mathematical literature in a well-organized,accessible format.After introducing the subject through a discussion of the basic results of linear functionalanalysis, this unique book proceeds to investigate the characteristics of strictly convexspaces and related classes, including uniformly convex spaces, and examine important applicationsregarding approximation theory and fixed point theory. Following this extensivetreatment, the book discusses complex strictly convex spaces and related spaces- alsowith applications. Complete, clearly elucidated proofs accompany results throughout thebook, and ample references are provided to aid further research of the subject.Strict Convexity and Complex Strict Convexity is essential fot mathematicians and studentsinterested in geometric theory of Banach spaces and applications to approximationtheory and fixed point theory, and is of great value to engineers working in optimizationstudies. In addition, this volume serves as an excellent text for a graduate course inGeometric Theory of Banach Spaces.
Book Synopsis Infinite-Dimensional Optimization and Convexity by : Ivar Ekeland
Download or read book Infinite-Dimensional Optimization and Convexity written by Ivar Ekeland and published by University of Chicago Press. This book was released on 1983-09-15 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The caratheodory approach; Infinite-dimensional optimization; Duality theory.
Book Synopsis Metric Spaces, Convexity and Nonpositive Curvature by : Athanase Papadopoulos
Download or read book Metric Spaces, Convexity and Nonpositive Curvature written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2005 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
