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Theory Of Convex Structures


Theory Of Convex Structures
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Theory Of Convex Structures


Theory Of Convex Structures
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Author : M.L.J. van de Vel
language : en
Publisher: Elsevier
Release Date : 1993-08-02

Theory Of Convex Structures written by M.L.J. van de Vel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-02 with Mathematics categories.


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.



Convex Structures And Economic Theory


Convex Structures And Economic Theory
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Author : Hukukane Nikaidō
language : en
Publisher: Elsevier
Release Date : 1968

Convex Structures And Economic Theory written by Hukukane Nikaidō and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Business & Economics categories.


This book 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.



Convex Bodies The Brunn Minkowski Theory


Convex Bodies The Brunn Minkowski Theory
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Author : Rolf Schneider
language : en
Publisher: Cambridge University Press
Release Date : 2014

Convex Bodies The Brunn Minkowski Theory written by Rolf Schneider and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.


A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.



Convex Structures And Economic Theory


Convex Structures And Economic Theory
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Author : Hukukane Nikaido
language : en
Publisher: Elsevier
Release Date : 2016-06-03

Convex Structures And Economic Theory written by Hukukane Nikaido and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.


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.



Convex Optimization


Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08

Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.


Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.



Mathematical Topics On Representations Of Ordered Structures And Utility Theory


Mathematical Topics On Representations Of Ordered Structures And Utility Theory
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Author : Gianni Bosi
language : en
Publisher: Springer Nature
Release Date : 2020-01-23

Mathematical Topics On Representations Of Ordered Structures And Utility Theory written by Gianni Bosi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Technology & Engineering categories.


This book offers an essential review of central theories, current research and applications in the field of numerical representations of ordered structures. It is intended as a tribute to Professor Ghanshyam B. Mehta, one of the leading specialists on the numerical representability of ordered structures, and covers related applications to utility theory, mathematical economics, social choice theory and decision-making. Taken together, the carefully selected contributions provide readers with an authoritative review of this research field, as well as the knowledge they need to apply the theories and methods in their own work.



Convex Analysis


Convex Analysis
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Author : Georgii G. Magaril-Ilʹyaev
language : en
Publisher: American Mathematical Soc.
Release Date :

Convex Analysis written by Georgii G. Magaril-Ilʹyaev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.


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.



Convexity And Optimization In Banach Spaces


Convexity And Optimization In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-03

Convexity And Optimization In Banach Spaces written by Viorel Barbu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-03 with Mathematics categories.


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.



Convex Analysis And Nonlinear Optimization


Convex Analysis And Nonlinear Optimization
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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-30

Convex Analysis And Nonlinear Optimization written by Jonathan M. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-30 with Mathematics categories.


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.



Finite Dimensional Convexity And Optimization


Finite Dimensional Convexity And Optimization
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Author : Monique Florenzano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite Dimensional Convexity And Optimization written by Monique Florenzano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study.