Download or read book Very Large scale Linear Programming a Case Study in Combining Interior Point and Simplex Methods written by R. E. Bixby and published by . This book was released on 1991 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Download or read book Large Scale Crew Scheduling written by Silke Jütte and published by Springer. This book was released on 2019-02-02 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decades, freight transportation experienced a worldwide boom. At the same time, competition increased considerably, such that efficient cost structures are indispensable for any market player. One of the main challenges a transportation company faces is the efficient employment of its personnel in operations, commonly referred to as crew scheduling. In this book the author presents solution approaches to large-scale crew scheduling. Firstly, the implementation of state-of-the-art operations research methods for a setting at a major European freight railway carrier is presented. Secondly, the author discusses acceleration techniques that make the developed algorithms applicable even in short-term contexts. While the analysis is based on European freight railway settings, the gained insights also apply to other (crew) scheduling contexts. Potential readership includes scholars and graduate students who are interested in the fields of crew scheduling and column generation as well as practitioners from transportation companies looking for new planning approaches.
Download or read book Numerical Analysis 1993 written by D.F. Griffiths and published by CRC Press. This book was released on 2020-10-07 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.
Download or read book Linear Programming 2 written by George B. Dantzig and published by Springer Science & Business Media. This book was released on 2006-04-28 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.
Download or read book Large Scale Computation and Information Processing in Air Traffic Control written by Lucio Bianco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compendium of papers presented during an Advanced Seminar on Air Traffic Control (ATC) that took place in Capri, Italy on October 28-31, 1991. The Seminar was' organized by the Progetto Finalizzato Trasporti of the Italian National Research Council. The papers presented in the Seminar dealt with a wide range of topics which are currently important in ATC. For example, there were papers on such subjects as recent developments in primary and secondary radar technologies, communications networks and protocols, and the future uses of satellite-based communications, navigation and surveillance in ATC. However, all the papers contained in the volume were selected exclusively from that set of papers that addressed some aspect of the main area of emphasis in the Seminar, namely massive data-processing requirements and computer intensive problems in ATC. Data-processing requirements in A TC have grown enormously over the years. Obviously, the rapid increase in air traffic volumes in most of the world is one of the factors that has contributed to this growth. However, two other developments have contributed much more significantly: first, the ATC system now collects (mostly automatically) immensely more "information per flight" than in the past; and, second, as the system's complexity increases and as it becomes more tightly interconnected geographically, so grows the need to communicate, process and "filter" the data presented to the system's various components.
Download or read book Interior Point Techniques in Optimization written by B. Jansen and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography. Audience: The book is intended for students, researchers and practitioners with a background in operations research, mathematics, mathematical programming, or statistics.
Download or read book Interior Point Algorithms written by Yinyu Ye and published by John Wiley & Sons. This book was released on 2011-10-11 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms: * Derives various complexity results for linear and convexprogramming * Emphasizes interior point geometry and potential theory * Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques * Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.
Download or read book Column Generation written by Guy Desaulniers and published by Springer Science & Business Media. This book was released on 2005-04-20 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
Download or read book Linear and Nonlinear Optimization written by Igor Griva and published by SIAM. This book was released on 2009-01-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.
Download or read book Handbook on Semidefinite Conic and Polynomial Optimization written by Miguel F. Anjos and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 955 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.
Download or read book Combinatorial Optimization written by William Cook and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a carefully refereed collection of invited survey articles written by outstanding researchers. Aimed at researchers in discrete mathematics, operations research, and the theory of computing, this book offers an in-depth look at many topics not treated in textbooks.
Download or read book Exploring Interior point Linear Programming written by Ami Arbel and published by MIT Press. This book was released on 1993 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides practitioners as well as students of this general methodology with an easily accessible introduction to the new class of algorithms known as interior-point methods for linear programming.
Download or read book Optimization Methods and Applications written by Xiao-qi Yang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book is dedicated to Professor N. U. Ahmed, a leading scholar and a renowned researcher in optimal control and optimization on the occasion of his retirement from the Department of Electrical Engineering at University of Ottawa in 1999. The contributions of this volume are in the areas of optimal control, non linear optimization and optimization applications. They are mainly the im proved and expanded versions of the papers selected from those presented in two special sessions of two international conferences. The first special session is Optimization Methods, which was organized by K. L. Teo and X. Q. Yang for the International Conference on Optimization and Variational Inequality, the City University of Hong Kong, Hong Kong, 1998. The other one is Optimal Control, which was organized byK. ~Teo and L. Caccetta for the Dynamic Control Congress, Ottawa, 1999. This volume is divided into three parts: Optimal Control; Optimization Methods; and Applications. The Optimal Control part is concerned with com putational methods, modeling and nonlinear systems. Three computational methods for solving optimal control problems are presented: (i) a regularization method for computing ill-conditioned optimal control problems, (ii) penalty function methods that appropriately handle final state equality constraints, and (iii) a multilevel optimization approach for the numerical solution of opti mal control problems. In the fourth paper, the worst-case optimal regulation involving linear time varying systems is formulated as a minimax optimal con trol problem.
Download or read book Acta Numerica 1993 Volume 2 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1993-04-30 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the tradition established with the 1992 volume, this 1993's Acta Numerica presents six invited papers on a broad range of topics from numerical analysis. Papers treat each topic at a level intelligible by any numerical analyst from graduate student to professional.
Download or read book Computer Science and Operations Research New Developments in their Interfaces written by Osman Balci and published by Elsevier. This book was released on 2014-05-23 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interface of Operation Research and Computer Science - although elusive to a precise definition - has been a fertile area of both methodological and applied research. The papers in this book, written by experts in their respective fields, convey the current state-of-the-art in this interface across a broad spectrum of research domains which include optimization techniques, linear programming, interior point algorithms, networks, computer graphics in operations research, parallel algorithms and implementations, planning and scheduling, genetic algorithms, heuristic search techniques and data retrieval.
