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Solving Staircase Linear Programs By The Simplex Method 1 Inversion
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Book Synopsis Solving staircase linear programs by the simplex method, 1: inversion by : Stanford University. Systems Optimization Laboratory
Download or read book Solving staircase linear programs by the simplex method, 1: inversion written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1979 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems of economic planning, production scheduling, inventory, transportation, control and multi-stage structural design have been modeled as linear programs that have a 'staircase' structure: their activities fall into a sequence of disjoint stages or periods, while their constraints relate only successive periods. At one time it was hoped that staircase linear programs would be particularly easy to solve, owing to their special structure, but experience with the most common solution technique -- the general simplex method -- has shown otherwise. Over the years many alternatives to the simplex method have also been proposed, but as yet none of these has been proved superior in solving a wide variety of staircase problems. This and a companion paper consider how the modern simplex method -- as implemented for large computers -- may be adapted to solve staircase linear programs more efficiently. Each paper looks at a set of algorithms within the simplex method: this one deals with 'inversion' of the basis -- more accurately, solution of linear systems by Gaussian elimination -- and its successor considers the task of 'pricing'.
Book Synopsis Linear Programming: An Introduction to Finite Improvement Algorithms by : Daniel Solow
Download or read book Linear Programming: An Introduction to Finite Improvement Algorithms written by Daniel Solow and published by Courier Corporation. This book was released on 2014-08-11 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Book Synopsis The Basic George B. Dantzig by : George Bernard Dantzig
Download or read book The Basic George B. Dantzig written by George Bernard Dantzig and published by Stanford University Press. This book was released on 2003 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The late George B. Dantzig , widely known as the father of linear programming, was a major influence in mathematics, operations research, and economics. As Professor Emeritus at Stanford University, he continued his decades of research on linear programming and related subjects. Dantzig was awarded eight honorary doctorates, the National Medal of Science, and the John von Neumann Theory Prize from the Institute for Operations Research and the Management Sciences. The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, non-technical summaries at the opening of each major section introduce a specific research area and discuss the current significance of Dantzig's work in that field. Among the topics covered are mathematical statistics, the Simplex Method of linear programming, economic modeling, network optimization, and nonlinear programming. The book also includes a complete bibliography of Dantzig's writings.
Book Synopsis Progress in Combinatorial Optimization by : William R. Pulleyblank
Download or read book Progress in Combinatorial Optimization written by William R. Pulleyblank and published by Academic Press. This book was released on 2014-05-10 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.
Book Synopsis Algorithms and Model Formulations in Mathematical Programming by : Stein W. Wallace
Download or read book Algorithms and Model Formulations in Mathematical Programming written by Stein W. Wallace and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Research Workshop (ARW) "Algorithms and Model Formulations in Mathematical Programming" was held at Chr. Michelsen Institute in Bergen, Norway, from June 15 to June 19, 1987. The ARW was organized on behalf of the Committee on Algorithms (COAL) of the Mathematical Programming Society (MPS). Co-directors were Jan Telgen (Van Dien+Co Organisatie, Utrecht, The Netherlands) and Roger J-B Wets (The University of California at Davis, USA). 43 participants from 11 countries attended the ARW. The workshop was organized such that each day started with a - minute keynote presentation, followed by a 45-minute plenary discussion. The first part of this book contains the contributions of the five keynote speakers. The plenary discussions were taped, and the transcripts given to the keynote speakers. They have treated the transcripts differently, some by working the discussions into their papers, others by adding a section which sums up the discussions. The plenary discussions were very interesting and stimulating due to active participation of the audience. The five keynote speakers were asked to view the topic of the workshop, the interaction between algorithms and model formulations, from different perspectives. On the first day of the workshop Professor Alexander H.G. Rinnooy Kan (Erasmus University, Rotterdam, The Netherlands) put the theme into a larger context by his talk "Mathematical programming as an intellectual activity". This is an article of importance to any mathematical programmer who is interested in his field's history and present state.
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 The Guided Decomposition Algorithm for Linear Programs by : David Frederick Lynch
Download or read book The Guided Decomposition Algorithm for Linear Programs written by David Frederick Lynch and published by . This book was released on 1984 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1981 with total page 1370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
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 Science & Business Media. This book was released on 2014-03-27 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods. In particular, it covers the determination of the optimal solution set, feasible-point simplex method, decomposition principle for solving large-scale problems, controlled-branch method based on generalized reduced simplex framework for solving integer LP problems.
Book Synopsis Linear Programming 1 by : George B. Dantzig
Download or read book Linear Programming 1 written by George B. Dantzig and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encompassing all the major topics students will encounter in courses on the subject, the authors teach both the underlying mathematical foundations and how these ideas are implemented in practice. They illustrate all the concepts with both worked examples and plenty of exercises, and, in addition, provide software so that students can try out numerical methods and so hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors' note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date, currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States option . The new version of Formula One, when ready, will be posted on WWW.
Book Synopsis Mathematical Programming by : Richard Cottle
Download or read book Mathematical Programming written by Richard Cottle and published by . This book was released on 1985 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Programming by : Saul I. Gass
Download or read book Linear Programming written by Saul I. Gass and published by Courier Corporation. This book was released on 2003-01-01 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive, well-organized volume, suitable for undergraduates, covers theoretical, computational, and applied areas in linear programming. Expanded, updated edition; useful both as a text and as a reference book. 1995 edition.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on 1980 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Time-staged linear programs by : Stanford University. Systems Optimization Laboratory
Download or read book Time-staged linear programs written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1980 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper outlines some procedures for solving time-staged (staircase) linear programs. Two approaches are discussed: the first based on modifying the block structure of the basis so that there are square non-singular sub-blocks along the diagonal; and the second based on the nested decomposition principle except applied to the dual system instead of the primal as proposed by Glassey and by Manne and Ho. (Author).
Book Synopsis Sparse Gaussian elimination of staircase linear systems by : Stanford University. Systems Optimization Laboratory
Download or read book Sparse Gaussian elimination of staircase linear systems written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1979 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: A square system of linear equations is said to be sparse if it can be solved most efficiently through a knowledge of its arrangement of zero and nonzero coefficients. Sparse systems are commonly solved by the techniques of sparse Gaussian elimination. An important class of sparse systems are those that have a 'staircase' structure: their variables fall into a natural sequence of disjoint groups, and each equation relates only variables within the group or within two adjacent groups. This paper proposes special methods of sparse Gaussian elimination for staircase-structured systems. These methods are particularly applicable to linear programming problems whose constraints have a staircase structure; they may also find application in solving staircase linear systems that arise in nonlinear optimization and optimal control. The initial sections of this paper present a self-contained review of sparse elimination, and derive pertinent properties of staircase systems. Subsequent sections pursue two approaches to staircase elimination, and report initial computational experience in detail. (Author).
Book Synopsis Advances in a Nested Decomposition Algorithm for Solving Staircase Linear Programs by : Stanford University. Systems Optimization Laboratory
Download or read book Advances in a Nested Decomposition Algorithm for Solving Staircase Linear Programs written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1983 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Government Reports Announcements & Index by :
Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1980 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt:
