Decomposition Techniques In Mathematical Programming
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Decomposition Techniques In Mathematical Programming
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Author : Antonio J. Conejo
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-28
Decomposition Techniques In Mathematical Programming written by Antonio J. Conejo 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 2006-04-28 with Technology & Engineering categories.
Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.
Adaptation Of Decomposition Methods To Some Transportation Problems
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Author : Kurt O. Jörnsten
language : en
Publisher:
Release Date : 1980
Adaptation Of Decomposition Methods To Some Transportation Problems written by Kurt O. Jörnsten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Decomposition method categories.
Mathematical Programming Methods
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Author : G. Zoutendijk
language : en
Publisher:
Release Date : 1976
Mathematical Programming Methods written by G. Zoutendijk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Theory of linear programming; The simplex method; Numerical aspects of the simplex method; Other methods for linear programming; Special structures; Post-optimal analysis; Decomposition and partitioning methods; Integer and mixed integer linear programming; Theory of nonlinear programming; General principles of a method of feasible directions; Direction generators; Linear programming and the methods of feasible directions; Unconstrained optimization; Quadratic programming; Linearly constrained nonlinear programming; General nonlinear programming.
Progress In Mathematical Programming
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Author : Nimrod Megiddo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Progress In Mathematical Programming written by Nimrod Megiddo 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 Mathematics categories.
The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."
Stochastic Decomposition
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Author : Julia L. Higle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Stochastic Decomposition written by Julia L. Higle 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 2013-11-27 with Mathematics categories.
Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.
Matheuristics
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Author : Vittorio Maniezzo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-18
Matheuristics written by Vittorio Maniezzo 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 2009-09-18 with Business & Economics categories.
Metaheuristics support managers in decision-making with robust tools that provide high-quality solutions to important applications in business, engineering, economics, and science in reasonable time frames, but finding exact solutions in these applications still poses a real challenge. However, because of advances in the fields of mathematical optimization and metaheuristics, major efforts have been made on their interface regarding efficient hybridization. This edited book will provide a survey of the state of the art in this field by providing some invited reviews by well-known specialists as well as refereed papers from the second Matheuristics workshop to be held in Bertinoro, Italy, June 2008. Papers will explore mathematical programming techniques in metaheuristics frameworks, and especially focus on the latest developments in Mixed Integer Programming in solving real-world problems.
Interior Point Techniques In Optimization
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Author : B. Jansen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Interior Point Techniques In Optimization written by B. Jansen 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 2013-03-14 with Mathematics categories.
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.
Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming
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Author : Ivo Nowak
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-28
Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming written by Ivo Nowak 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 2006-03-28 with Computers categories.
Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: • A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. • In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. • The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.
Enterprise Collaboration
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Author : David M. Levermore
language : en
Publisher: Springer
Release Date : 2008-11-01
Enterprise Collaboration written by David M. Levermore and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Business & Economics categories.
This book goes beyond the discussion of global databases and presents a general Enterprise Resources Market model to facilitate the management and integration of enterprise information resources in a cooperating mode. It is the first book to analyze the problem from the perspective of information management and to present a solution for a key aspect of the cooperation problem—on-demand information exchange.
Proceedings Of The Princeton Symposium On Mathematical Programming
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Author : Harold William Kuhn
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Proceedings Of The Princeton Symposium On Mathematical Programming written by Harold William Kuhn and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Mathematics categories.
This volume contains thirty-three selected general research papers devoted to the theory and application of the mathematics of constrained optimization, including linear programming and its extensions to convex programming, general nonlinear programming, integer programming, and programming under uncertainty. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.