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Large Scale Linear Programming


Large Scale Linear Programming
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Large Scale Linear And Integer Optimization A Unified Approach


Large Scale Linear And Integer Optimization A Unified Approach
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Author : Richard Kipp Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 1999

Large Scale Linear And Integer Optimization A Unified Approach written by Richard Kipp Martin 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 1999 with Business & Economics categories.


In this book, Kipp Martin has systematically provided users with a unified treatment of the algorithms and the implementation of the algorithms that are important in solving large problems. Parts I and II of Large Scale Linear and Integer Programming provide an introduction to linear optimization using two simple but unifying ideas-projection and inverse projection. The ideas of projection and inverse projection are also extended to integer linear optimization. With the projection-inverse projection approach, theoretical results in integer linear optimization become much more analogous to their linear optimization counterparts. Hence, with an understanding of these two concepts, the reader is equipped to understand fundamental theorems in an intuitive way. Part III presents the most important algorithms that are used in commercial software for solving real-world problems. Part IV shows how to take advantage of the special structure in very large scale applications through decomposition. Part V describes,how to take advantage of special structure by modifying and enhancing the algorithms developed in Part III. This section contains a discussion of the current research in linear and integer linear programming. The author also shows in Part V how to take different problem formulations and appropriately 'modify' them so that the algorithms from Part III are more efficient. Again, the projection and inverse projection concepts are used in Part V to present the current research in linear and integer linear optimization in a very unified way.



Large Scale Linear And Integer Optimization A Unified Approach


Large Scale Linear And Integer Optimization A Unified Approach
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Author : Richard Kipp Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Large Scale Linear And Integer Optimization A Unified Approach written by Richard Kipp Martin 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 Business & Economics categories.


This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.



Large Scale Linear Programming


Large Scale Linear Programming
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Author : George Bernard Dantzig
language : en
Publisher:
Release Date : 1981

Large Scale Linear Programming written by George Bernard Dantzig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Linear programming categories.




Large Scale Linear Programming Problems


Large Scale Linear Programming Problems
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Author : AFAF. FOUAD NAKHLA
language : en
Publisher:
Release Date : 1978

Large Scale Linear Programming Problems written by AFAF. FOUAD NAKHLA and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.




Large Scale Optimization


Large Scale Optimization
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Author : Vladimir Tsurkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03-31

Large Scale Optimization written by Vladimir Tsurkov 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 2001-03-31 with Computers categories.


Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.



Solving Large Scale Linear Programming By Iterative Methods


Solving Large Scale Linear Programming By Iterative Methods
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Author : Chee Hwee Seah
language : en
Publisher:
Release Date : 2000

Solving Large Scale Linear Programming By Iterative Methods written by Chee Hwee Seah and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.




Robust Reduction Of Large Scale Linear Programming Problems


Robust Reduction Of Large Scale Linear Programming Problems
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Author :
language : en
Publisher:
Release Date : 1996

Robust Reduction Of Large Scale Linear Programming Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.




A Numerical Investigation Of Ellipsoid Algorithms For Large Scale Linear Programming


A Numerical Investigation Of Ellipsoid Algorithms For Large Scale Linear Programming
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Author : Stanford University. Systems Optimization Laboratory
language : en
Publisher:
Release Date : 1980

A Numerical Investigation Of Ellipsoid Algorithms For Large Scale Linear Programming written by Stanford University. Systems Optimization Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.


The ellipsoid algorithm associated with Shor, Khachiyan and others has certain theoretical properties that suggest its use as a linear programming algorithm. Some of the practical difficulties are investigated here. A variant of the ellipsoid update is first developed, to take advantage of the range constraints that often occur in linear programs (i.e., constraints of the form l



Encyclopedia Of Optimization


Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04

Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.


The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".



Large Scale Linear Programming


Large Scale Linear Programming
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Author :
language : en
Publisher:
Release Date : 1981

Large Scale Linear Programming written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.