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Author: M.L.J. van de Vel Publisher: Elsevier ISBN: 0080933106 Category : Mathematics Languages : en Pages : 556
Book Description
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: M.L.J. van de Vel Publisher: Elsevier ISBN: 0080933106 Category : Mathematics Languages : en Pages : 556
Book Description
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: 1483266680 Category : Mathematics Languages : en Pages : 422
Book Description
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: Kazuo Murota Publisher: SIAM ISBN: 9780898718508 Category : Mathematics Languages : en Pages : 411
Book Description
Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.
Author: P. Pérez Carreras Publisher: Elsevier ISBN: 0080872425 Category : Mathematics Languages : en Pages : 529
Book Description
This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the space. The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and Br-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.
Author: Elimhan N Mahmudov Publisher: Elsevier ISBN: 0123884284 Category : Mathematics Languages : en Pages : 396
Book Description
Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples
Author: Richard M. Aron Publisher: CRC Press ISBN: 1482299100 Category : Mathematics Languages : en Pages : 324
Book Description
Renewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in Mathematics collects the main results on the conditions for
Author: Hiroshi Konno Publisher: Springer Science & Business Media ISBN: 1461540984 Category : Mathematics Languages : en Pages : 462
Book Description
Global optimization is one of the fastest developing fields in mathematical optimization. In fact, an increasing number of remarkably efficient deterministic algorithms have been proposed in the last ten years for solving several classes of large scale specially structured problems encountered in such areas as chemical engineering, financial engineering, location and network optimization, production and inventory control, engineering design, computational geometry, and multi-objective and multi-level optimization. These new developments motivated the authors to write a new book devoted to global optimization problems with special structures. Most of these problems, though highly nonconvex, can be characterized by the property that they reduce to convex minimization problems when some of the variables are fixed. A number of recently developed algorithms have been proved surprisingly efficient for handling typical classes of problems exhibiting such structures, namely low rank nonconvex structures. Audience: The book will serve as a fundamental reference book for all those who are interested in mathematical optimization.
Author: M.L.J. van de Vel
Author: M.L.J. van de Vel
Author: Hukukane Nikaido
Author: Wiesław Kubiś
Author: 
Author: Kazuo Murota
Author: P. Pérez Carreras
Author: Elimhan N Mahmudov
Author: Richard M. Aron
Author: Hiroshi Konno
Author: H.. Nikado