Theory Of Convex Structures PDF Download
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| Author | : M.L.J. van de Vel |
| Publisher | : Elsevier |
| Total Pages | : 556 |
| Release | : 1993-08-02 |
| Genre | : Mathematics |
| ISBN | : 0080933106 |
Download Theory of Convex Structures Book in PDF, ePub and Kindle
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 |
| Total Pages | : 422 |
| Release | : 2016-06-03 |
| Genre | : Mathematics |
| ISBN | : 1483266680 |
Download Convex Structures and Economic Theory Book in PDF, ePub and Kindle
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 |
| Total Pages | : 759 |
| Release | : 2014 |
| Genre | : Mathematics |
| ISBN | : 1107601010 |
Download Convex Bodies: The Brunn–Minkowski Theory Book in PDF, ePub and Kindle
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 |
| Total Pages | : 316 |
| Release | : 2010-05-05 |
| Genre | : Mathematics |
| ISBN | : 0387312560 |
Download Convex Analysis and Nonlinear Optimization Book in PDF, ePub and Kindle
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 | : Wiesław Kubiś |
| Publisher | : |
| Total Pages | : |
| Release | : 1999 |
| Genre | : |
| ISBN | : |
Download Abstract Convex Structures in Topology and Set Theory Book in PDF, ePub and Kindle
| Author | : Viorel Barbu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2012-01-03 |
| Genre | : Mathematics |
| ISBN | : 940072246X |
Download Convexity and Optimization in Banach Spaces Book in PDF, ePub and Kindle
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 | : |
| Publisher | : |
| Total Pages | : |
| Release | : 1997 |
| Genre | : |
| ISBN | : |
Download Convex Structures and Economic Theory Book in PDF, ePub and Kindle
| Author | : Paul J. Kelly |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2009 |
| Genre | : Convex bodies |
| ISBN | : 9780486469805 |
Download Geometry and Convexity Book in PDF, ePub and Kindle
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 | : Edgar Lee Stout |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 454 |
| Release | : 2007-05-03 |
| Genre | : Mathematics |
| ISBN | : 0817645373 |
Download Polynomial Convexity Book in PDF, ePub and Kindle
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.
| 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.
