Linear And Convex Programming
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Introduction To Linear And Convex Programming
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Author : Neil Cameron
language : en
Publisher: CUP Archive
Release Date : 1985-09-05
Introduction To Linear And Convex Programming written by Neil Cameron and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-09-05 with Mathematics categories.
This introduction to optimization emphasizes the need for both a pure and an applied mathematical point of view. Beginning with a chapter on linear algebra and Euclidean geometry, the author then applies this theory with an introduction to linear programming. There follows a discussion of convex analysis, which finds application in non-linear programming. The book ends with an extensive commentary to the exercises that are given at the end of each chapter. The author's straightforward, geometrical approach makes this an attractive textbook for undergraduate students of mathematics, engineering, operations research and economics.
Linear And Convex Programming
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Author : Semen Izrailevich Zukhovit︠s︡kiĭ
language : en
Publisher:
Release Date : 1966
Linear And Convex Programming written by Semen Izrailevich Zukhovit︠s︡kiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Convex programming categories.
Interior Point Approach To Linear Quadratic And Convex Programming
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Author : D. den Hertog
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Interior Point Approach To Linear Quadratic And Convex Programming written by D. den Hertog 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 describes the rapidly developing field of interior point methods (IPMs). An extensive analysis is given of path-following methods for linear programming, quadratic programming and convex programming. These methods, which form a subclass of interior point methods, follow the central path, which is an analytic curve defined by the problem. Relatively simple and elegant proofs for polynomiality are given. The theory is illustrated using several explicit examples. Moreover, an overview of other classes of IPMs is given. It is shown that all these methods rely on the same notion as the path-following methods: all these methods use the central path implicitly or explicitly as a reference path to go to the optimum. For specialists in IPMs as well as those seeking an introduction to IPMs. The book is accessible to any mathematician with basic mathematical programming knowledge.
Linear Programming
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Author : Robert J Vanderbei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Linear Programming written by Robert J Vanderbei 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 2013-06-29 with Business & Economics categories.
This book provides an introduction to optimization. It details constrained optimization, beginning with a substantial treatment of linear programming and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Coverage underscores the purpose of optimization: to solve practical problems on a computer. C programs that implement the major algorithms and JAVA tools are available online.
Interior Point Polynomial Algorithms In Convex Programming
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Author : Yurii Nesterov
language : en
Publisher: SIAM
Release Date : 1994-01-01
Interior Point Polynomial Algorithms In Convex Programming written by Yurii Nesterov and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
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.
High Performance Optimization
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Author : Hans Frenk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
High Performance Optimization written by Hans Frenk 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 2013-04-17 with Mathematics categories.
For a long time the techniques of solving linear optimization (LP) problems improved only marginally. Fifteen years ago, however, a revolutionary discovery changed everything. A new `golden age' for optimization started, which is continuing up to the current time. What is the cause of the excitement? Techniques of linear programming formed previously an isolated body of knowledge. Then suddenly a tunnel was built linking it with a rich and promising land, part of which was already cultivated, part of which was completely unexplored. These revolutionary new techniques are now applied to solve conic linear problems. This makes it possible to model and solve large classes of essentially nonlinear optimization problems as efficiently as LP problems. This volume gives an overview of the latest developments of such `High Performance Optimization Techniques'. The first part is a thorough treatment of interior point methods for semidefinite programming problems. The second part reviews today's most exciting research topics and results in the area of convex optimization. Audience: This volume is for graduate students and researchers who are interested in modern optimization techniques.
Conjugate Duality And Optimization
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Author : R. Tyrrell Rockafellar
language : en
Publisher: SIAM
Release Date : 1974-01-01
Conjugate Duality And Optimization written by R. Tyrrell Rockafellar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Technology & Engineering categories.
The theory of duality in problems of optimization is developed in a setting of finite and infinite dimensional spaces using convex analysis. Applications to convex and nonconvex problems. Expository account containing many new results. (Author).
Stochastic Linear Programming Algorithms
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Author : Janos Mayer
language : en
Publisher: CRC Press
Release Date : 1998-02-25
Stochastic Linear Programming Algorithms written by Janos Mayer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-25 with Computers categories.
A computationally oriented comparison of solution algorithms for two stage and jointly chance constrained stochastic linear programming problems, this is the first book to present comparative computational results with several major stochastic programming solution approaches. The following methods are considered: regularized decomposition, stochastic decomposition and successive discrete approximation methods for two stage problems; cutting plane methods, and a reduced gradient method for jointly chance constrained problems. The first part of the book introduces the algorithms, including a unified approach to decomposition methods and their regularized counterparts. The second part addresses computer implementation of the methods, describes a testing environment based on a model management system, and presents comparative computational results with the various algorithms. Emphasis is on the computational behavior of the algorithms.
Separable Programming
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Author : S.M. Stefanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Separable Programming written by S.M. Stefanov 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 2013-11-11 with Mathematics categories.
In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well. Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.