Theory Of Convex Structures

Author : M.L.J. van de Vel
Publisher : Elsevier
ISBN 13 : 0080933106
Total Pages : 539 pages
Book Rating : 4.08/5 ( download)

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Download or read book Theory of Convex Structures written by M.L.J. van de Vel and published by Elsevier. This book was released on 1993-08-02 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

Author : Hukukane Nikaido
Publisher : Elsevier
ISBN 13 : 1483266680
Total Pages : 422 pages
Book Rating : 4.88/5 ( download)

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Download or read book Convex Structures and Economic Theory written by Hukukane Nikaido and published by Elsevier. This book was released on 2016-06-03 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics in Science and Engineering, Volume 51: Convex Structures and Economic Theory consists of an account of the theory of convex sets and its application to several basic problems that originate in economic theory and adjacent subject matter. This volume includes examples of problems pertaining to interesting static and dynamic phenomena in linear and nonlinear economic systems, as well as models initiated by Leontief, von Neumann, and Walras. The topics covered are the mathematical theorems on convexity, simple multisector linear systems, balanced growth in nonlinear systems, and efficient allocation and growth. The working of Walrasian competitive economies, special features of competitive economies, and Jacobian matrix and global univalence are also covered. This publication is suitable for advanced students of mathematical economics and related fields, but is also beneficial for anyone who wishes to become familiar with the basic ideas, methods, and results in the mathematical treatment in economic theory through a detailed exposition of a number of typical representative problems.

Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 1107601010
Total Pages : 759 pages
Book Rating : 4.17/5 ( download)

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Download or read book Convex Bodies: The Brunn–Minkowski Theory written by Rolf Schneider and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.

Author : Jonathan Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 0387312560
Total Pages : 316 pages
Book Rating : 4.69/5 ( download)

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Download or read book Convex Analysis and Nonlinear Optimization written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Author : Viorel Barbu
Publisher : Springer Science & Business Media
ISBN 13 : 940072246X
Total Pages : 376 pages
Book Rating : 4.60/5 ( download)

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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.

Author : Wiesław Kubiś
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.82/5 ( download)

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Download or read book Abstract Convex Structures in Topology and Set Theory written by Wiesław Kubiś and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A.D. Alexandrov
Publisher : Springer Science & Business Media
ISBN 13 : 3540263403
Total Pages : 545 pages
Book Rating : 4.01/5 ( download)

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Download or read book Convex Polyhedra written by A.D. Alexandrov and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.

Author : Paul J. Kelly
Publisher :
ISBN 13 : 9780486469805
Total Pages : 0 pages
Book Rating : 4.08/5 ( download)

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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.

Author : Erhan Çınlar
Publisher : Springer Science & Business Media
ISBN 13 : 1461452570
Total Pages : 164 pages
Book Rating : 4.77/5 ( download)

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Download or read book Real and Convex Analysis written by Erhan Çınlar and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Edgar Lee Stout
Publisher : Springer Science & Business Media
ISBN 13 : 0817645373
Total Pages : 454 pages
Book Rating : 4.73/5 ( download)

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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.