Convexity And Optimization In Finite Dimensions Bd 1
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Author |
: Josef Stoer |
Publisher |
: |
Total Pages |
: 293 |
Release |
: 1970 |
ISBN-10 |
: OCLC:464029352 |
ISBN-13 |
: |
Rating |
: 4/5 (52 Downloads) |
Synopsis Convexity and Optimization in Finite Dimensions. Bd. 1 by : Josef Stoer
Author |
: Josef Stoer |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 306 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642462160 |
ISBN-13 |
: 3642462162 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Convexity and Optimization in Finite Dimensions I by : Josef Stoer
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.
Author |
: |
Publisher |
: |
Total Pages |
: 293 |
Release |
: 1970 |
ISBN-10 |
: OCLC:472266229 |
ISBN-13 |
: |
Rating |
: 4/5 (29 Downloads) |
Synopsis Convexity and Optimization in Finite Dimensions. Vol. 1 by :
Author |
: Monique Florenzano |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 161 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642565229 |
ISBN-13 |
: 3642565220 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Finite Dimensional Convexity and Optimization by : Monique Florenzano
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.
Author |
: Viorel Barbu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 376 |
Release |
: 2012-01-03 |
ISBN-10 |
: 9789400722460 |
ISBN-13 |
: 940072246X |
Rating |
: 4/5 (60 Downloads) |
Synopsis Convexity and Optimization in Banach Spaces by : Viorel Barbu
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 |
: Josef Stoer |
Publisher |
: |
Total Pages |
: |
Release |
: 1970 |
ISBN-10 |
: OCLC:473172665 |
ISBN-13 |
: |
Rating |
: 4/5 (65 Downloads) |
Synopsis Convexity and optimization in finite dimensions by : Josef Stoer
Author |
: Dan Butnariu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 230 |
Release |
: 2000 |
ISBN-10 |
: 079236287X |
ISBN-13 |
: 9780792362876 |
Rating |
: 4/5 (7X Downloads) |
Synopsis Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization by : Dan Butnariu
The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, total convexity, is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making a general approach possible the work aims to improve upon classical results like the Holder-Minkowsky inequality of ℒp.
Author |
: Josef Stoer |
Publisher |
: |
Total Pages |
: 293 |
Release |
: 1970 |
ISBN-10 |
: OCLC:1088806708 |
ISBN-13 |
: |
Rating |
: 4/5 (08 Downloads) |
Synopsis Convexity and Optimization in Finite Dimensions Volume I by : Josef Stoer
Author |
: Boris S. Mordukhovich |
Publisher |
: Springer Nature |
Total Pages |
: 597 |
Release |
: 2022-04-24 |
ISBN-10 |
: 9783030947859 |
ISBN-13 |
: 3030947858 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Convex Analysis and Beyond by : Boris S. Mordukhovich
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.
Author |
: Josef Stoer (Mathématicien) |
Publisher |
: |
Total Pages |
: 293 |
Release |
: 1970 |
ISBN-10 |
: OCLC:636604870 |
ISBN-13 |
: |
Rating |
: 4/5 (70 Downloads) |
Synopsis Convexity and optimization in finite dimensions I by : Josef Stoer (Mathématicien)