Decomposition Techniques In Mathematical Programming

Author : Antonio J. Conejo,Enrique Castillo,Roberto Minguez,Raquel Garcia-Bertrand
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 51,8 Mb
Release : 2006-04-28
Category : Technology & Engineering
ISBN : 9783540276869

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Decomposition Techniques in Mathematical Programming by Antonio J. Conejo,Enrique Castillo,Roberto Minguez,Raquel Garcia-Bertrand Pdf

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.

Author : Julia L. Higle,S. Sen
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 42,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461541158

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Stochastic Decomposition by Julia L. Higle,S. Sen Pdf

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.

Author : G. Zoutendijk
Publisher : Unknown
Page : 524 pages
File Size : 48,9 Mb
Release : 1976
Category : Mathematics
ISBN : UCAL:B4406042

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Mathematical Programming Methods by G. Zoutendijk Pdf

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.

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396178

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Progress in Mathematical Programming by Nimrod Megiddo Pdf

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."

Author : Kurt O. Jörnsten
Publisher : Unknown
Page : 398 pages
File Size : 41,9 Mb
Release : 1980
Category : Decomposition method
ISBN : NWU:35556021086228

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Adaptation of Decomposition Methods to Some Transportation Problems by Kurt O. Jörnsten Pdf

Author : Vladimir Tsurkov
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 42,5 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781475732436

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Large-scale Optimization by Vladimir Tsurkov Pdf

Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.

Author : David M. Levermore,Cheng Hsu
Publisher : Springer
Page : 176 pages
File Size : 52,5 Mb
Release : 2008-11-01
Category : Business & Economics
ISBN : 0387514295

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Enterprise Collaboration by David M. Levermore,Cheng Hsu Pdf

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.

Author : Kiyotaka Shimizu,Yo Ishizuka,Jonathan F. Bard
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461563051

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Nondifferentiable and Two-Level Mathematical Programming by Kiyotaka Shimizu,Yo Ishizuka,Jonathan F. Bard Pdf

The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.

Author : Harold William Kuhn
Publisher : Princeton University Press
Page : 627 pages
File Size : 45,6 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400869930

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Proceedings of the Princeton Symposium on Mathematical Programming by Harold William Kuhn Pdf

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.

Author : Enrique Castillo,Antonio J. Conejo,Pablo Pedregal,Ricardo García,Natalia Alguacil
Publisher : John Wiley & Sons
Page : 568 pages
File Size : 42,6 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9780471461654

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Building and Solving Mathematical Programming Models in Engineering and Science by Enrique Castillo,Antonio J. Conejo,Pablo Pedregal,Ricardo García,Natalia Alguacil Pdf

Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes: * Discussion and implementation of the GAMS programming system * Unique coverage of compatibility * Illustrative examples that showcase the connection between model and reality * Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises * Real-world applications to probability and statistics, electrical engineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.

Author : B. Jansen
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 40,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475755619

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Interior Point Techniques in Optimization by B. Jansen Pdf

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.

Author : Melvyn Jeter
Publisher : Routledge
Page : 194 pages
File Size : 42,6 Mb
Release : 2018-05-03
Category : Business & Economics
ISBN : 9781351433129

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Mathematical Programming by Melvyn Jeter Pdf

This book serves as an introductory text in mathematical programming and optimization for students having a mathematical background that includes one semester of linear algebra and a complete calculus sequence. It includes computational examples to aid students develop computational skills.

Author : Vittorio Maniezzo,Thomas Stützle,Stefan Voß
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 43,9 Mb
Release : 2009-09-18
Category : Business & Economics
ISBN : 9781441913067

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Matheuristics by Vittorio Maniezzo,Thomas Stützle,Stefan Voß Pdf

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.

Author : Ivo Nowak
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 41,9 Mb
Release : 2006-03-28
Category : Computers
ISBN : 9783764373740

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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming by Ivo Nowak Pdf

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.

Author : T. C. Hu,Stephen M. Robinson
Publisher : Academic Press
Page : 308 pages
File Size : 55,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260792

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Mathematical Programming by T. C. Hu,Stephen M. Robinson Pdf

Mathematical Programming provides information pertinent to the developments in mathematical programming. This book covers a variety of topics, including integer programming, dynamic programming, game theory, nonlinear programming, and combinatorial equivalence. Organized into nine chapters, this book begins with an overview of optimization of very large-scale planning problems that can be achieved on significant problems. This text then introduces non-stationary policies and determines certain operating characteristics of the optimal policy for a very long planning horizon. Other chapters consider the perfect graph theorem by defining some well-known integer-valued functions of an arbitrary graph. This book discusses as well integer programming that deals with the class of mathematical programming problems in which some or all of the variables are required to be integers. The final chapter deals with the basic theorem of game theory. This book is a valuable resource for readers who are interested in mathematical programming. Mathematicians will also find this book useful.