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The Factorization Approach To Large Scale Linear Programming
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Book Synopsis The Factorization Approach to Large-Scale Linear Programming by : W. G. Graves
Download or read book The Factorization Approach to Large-Scale Linear Programming written by W. G. Graves and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Factorization Approach to Large-Scale Linear Programming by : G. W. Graves
Download or read book The Factorization Approach to Large-Scale Linear Programming written by G. W. Graves and published by . This book was released on 1973 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unifying concept for large-scale linear programming is developed. This approach called 'factorization' allows one to isolate the effect of different types of constraints and variables in the algebraic representation of the tableau. Two different factorizations based on a double representation of the basic tableau are presented. The use of factorization to obtain efficient algorithms for generalized upper bounding and block diagonal constraints as well as the general network problem is discussed. Computational results for a new network algorithm based on factorization are presented. (Author).
Book Synopsis Large-scale Numerical Optimization by : Thomas Frederick Coleman
Download or read book Large-scale Numerical Optimization written by Thomas Frederick Coleman and published by SIAM. This book was released on 1990-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.
Book Synopsis Factorization in Large-scale Linear Programming by : Richard DeWayne McBride
Download or read book Factorization in Large-scale Linear Programming written by Richard DeWayne McBride and published by . This book was released on 1973 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Dynamic Factorization Algorithm for General Large-Scale Linear Programming Problems by : Richard D. McBride
Download or read book A Dynamic Factorization Algorithm for General Large-Scale Linear Programming Problems written by Richard D. McBride and published by . This book was released on 1977 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin
Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis FACTORIZATION IN LARGE-SCALE LINEAR PROGRAMMING by : RICHARD D. MACBRIDE
Download or read book FACTORIZATION IN LARGE-SCALE LINEAR PROGRAMMING written by RICHARD D. MACBRIDE and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Large-scale Linear Programming Using the Cholesky Factorization by : M. A. Saunders
Download or read book Large-scale Linear Programming Using the Cholesky Factorization written by M. A. Saunders and published by . This book was released on 1972 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Large-scale Linear Programming by : Markku Juhani Kallio
Download or read book On Large-scale Linear Programming written by Markku Juhani Kallio and published by . This book was released on 1975 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three classes of methods are proposed for solving large-scale linear programs. First, sequential projection is applied to reformulate the linear program as a dynamic program. Second, the revised simplex method using a special factorization for the basis is considered. Third, a class of feasible direction methods is presented. A comparison of these three classes is made. A probabilistic model is developed to estimate computational effort for matrix multiplications. This model is applied to estimate computational effort for linear programming algorithms.
Book Synopsis Dynamic Factorization in Large-Scale Optimization by : Michael P. Olson
Download or read book Dynamic Factorization in Large-Scale Optimization written by Michael P. Olson and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factorization is an approach to linear programming (LP) in which the algebraic elements of the LP tableau are organized in such a way that a large portion of the tableau may be represented implicitly and generated from the remaining explicit part. In dynamic row factorization, the row structure of the LP model instance influences the algebraic structure of the tableau, and the dimension of the algebraic elements may change as the solution progresses. We present three algorithms motivated by this approach, each resulting from a different LPL model row structure: generalized upper bound (GUB) rows, pure network rows and generalized network rows. We describe implementations of all three algorithms, specifying data structures for tableau and basis inverse representations and detailing procedures for manipulation and update of these representations. (KR).
Book Synopsis Dynamic Factorization in Large-Scale Optimization by : Michael P. Olson
Download or read book Dynamic Factorization in Large-Scale Optimization written by Michael P. Olson and published by . This book was released on 1989 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factorization is an approach to linear programming (LP) in which the algebraic elements of the LP tableau are organized in such a way that a large portion of the tableau may be represented implicitly and generated from the remaining explicit part. In dynamic row factorization, the row structure of the LP model instance influences the algebraic structure of the tableau, and the dimension of the algebraic elements may change as the solution progresses. We present three algorithms motivated by this approach, each resulting from a different LPL model row structure: generalized upper bound (GUB) rows, pure network rows and generalized network rows. We describe implementations of all three algorithms, specifying data structures for tableau and basis inverse representations and detailing procedures for manipulation and update of these representations. (KR).
Book Synopsis Large-scale Linear Programming by : George Bernard Dantzig
Download or read book Large-scale Linear Programming written by George Bernard Dantzig and published by . This book was released on 1981 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computer Model for Solving Large Linear Programming Problems Using the Factorization Approach by : Kailash Chandra Sharma
Download or read book Computer Model for Solving Large Linear Programming Problems Using the Factorization Approach written by Kailash Chandra Sharma and published by . This book was released on 1976 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solution of Large Scale Pipe Networks by Improved Mathematical Approaches by :
Download or read book Solution of Large Scale Pipe Networks by Improved Mathematical Approaches written by and published by . This book was released on 1978 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Programming Computation by : Ping-Qi PAN
Download or read book Linear Programming Computation written by Ping-Qi PAN and published by Springer Nature. This book was released on 2023-01-01 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph represents a historic breakthrough in the field of linear programming (LP)since George Dantzig first discovered the simplex method in 1947. Being both thoughtful and informative, it focuses on reflecting and promoting the state of the art by highlighting new achievements in LP. This new edition is organized in two volumes. The first volume addresses foundations of LP, including the geometry of feasible region, the simplex method and its implementation, duality and the dual simplex method, the primal-dual simplex method, sensitivity analysis and parametric LP, the generalized simplex method, the decomposition method, the interior-point method and integer LP method. The second volume mainly introduces contributions of the author himself, such as efficient primal/dual pivot rules, primal/dual Phase-I methods, reduced/D-reduced simplex methods, the generalized reduced simplex method, primal/dual deficient-basis methods, primal/dual face methods, a new decomposition principle, etc. Many important improvements were made in this edition. The first volume includes new results, such as the mixed two-phase simplex algorithm, dual elimination, fresh pricing scheme for reduced cost, bilevel LP models and intercepting of optimal solution set. In particular, the chapter Integer LP Method was rewritten with great gains of the objective cutting for new ILP solvers {\it controlled-cutting/branch} methods, as well as with an attractive implementation of the controlled-branch method. In the second volume, the `simplex feasible-point algorithm' was rewritten, and removed from the chapter Pivotal Interior-Point Method to form an independent chapter with the new title `Simplex Interior-Point Method', as it represents a class of efficient interior-point algorithms transformed from traditional simplex algorithms. The title of the original chapter was then changed to `Facial Interior-Point Method', as the remaining algorithms represent another class of efficient interior-point algorithms transformed from normal interior-point algorithms. Without exploiting sparsity, the original primal/dual face methods were implemented using Cholesky factorization. In order to deal with sparse computation, two new chapters discussing LU factorization were added to the second volume. The most exciting improvement came from the rediscovery of the reduced simplex method. In the first edition, the derivation of its prototype was presented in a chapter with the same title, and then converted into the so-called `improved' version in another chapter. Fortunately, the author recently found a quite concise new derivation, so he can now introduce the distinctive fresh simplex method in a single chapter. It is exciting that the reduced simplex method can be expected to be the best LP solver ever. With a focus on computation, the current edition contains many novel ideas, theories and methods, supported by solid numerical results. Being clear and succinct, its content reveals in a fresh manner, from simple to profound. In particular, a larger number of examples were worked out to demonstrate algorithms. This book is a rare work in LP and an indispensable tool for undergraduate and graduate students, teachers, practitioners, and researchers in LP and related fields.
Author :Christodoulos A. Floudas Publisher :Springer Science & Business Media ISBN 13 :0387747583 Total Pages :4646 pages Book Rating :4.3/5 (877 download)
Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Book Synopsis Parallel Solution of Large-scale Optimization Problems by : Robert Stephen Maier
Download or read book Parallel Solution of Large-scale Optimization Problems written by Robert Stephen Maier and published by . This book was released on 1990 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: