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Large Scale Linear Programming Using The Cholesky Factorization
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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 Product Form of the Cholesky Factorization for Large-scale Linear Programming by : Stanford University. Computer Science Department
Download or read book Product Form of the Cholesky Factorization for Large-scale Linear Programming written by Stanford University. Computer Science Department and published by . This book was released on 1972 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Advanced Implementation of Cholesky Factorization for Computing Projections in Interior Point Methods of Large Scale Linear Programming by : Jacek Gondzio
Download or read book An Advanced Implementation of Cholesky Factorization for Computing Projections in Interior Point Methods of Large Scale Linear Programming written by Jacek Gondzio and published by . This book was released on 1991 with total page 29 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.
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 A numerical investigation of ellipsoid algorithms for large scale linear programming by : Stanford University. Systems Optimization Laboratory
Download or read book A numerical investigation of ellipsoid algorithms for large scale linear programming written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1980 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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 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 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 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 Linear Algebra for Large Scale and Real-Time Applications by : M.S. Moonen
Download or read book Linear Algebra for Large Scale and Real-Time Applications written by M.S. Moonen and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992
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 On Large-scale Linear Programming by : Stanford University. Systems Optimization Laboratory
Download or read book On Large-scale Linear Programming written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1975 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Studies in Large-scale Optimization by : Chih-Jen Lin
Download or read book Studies in Large-scale Optimization written by Chih-Jen Lin and published by . This book was released on 1998 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Nested Decomposition of Large Scale Linear Programs with the Staircase Structure by : James Kar-Yew Ho
Download or read book Nested Decomposition of Large Scale Linear Programs with the Staircase Structure written by James Kar-Yew Ho and published by . This book was released on 1974 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Programming by : Romesh Saigal
Download or read book Linear Programming written by Romesh Saigal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Linear Programming: A Modern Integrated Analysis, both boundary (simplex) and interior point methods are derived from the complementary slackness theorem and, unlike most books, the duality theorem is derived from Farkas's Lemma, which is proved as a convex separation theorem. The tedium of the simplex method is thus avoided. A new and inductive proof of Kantorovich's Theorem is offered, related to the convergence of Newton's method. Of the boundary methods, the book presents the (revised) primal and the dual simplex methods. An extensive discussion is given of the primal, dual and primal-dual affine scaling methods. In addition, the proof of the convergence under degeneracy, a bounded variable variant, and a super-linearly convergent variant of the primal affine scaling method are covered in one chapter. Polynomial barrier or path-following homotopy methods, and the projective transformation method are also covered in the interior point chapter. Besides the popular sparse Cholesky factorization and the conjugate gradient method, new methods are presented in a separate chapter on implementation. These methods use LQ factorization and iterative techniques.