On The Unboundedness Of The Set Of Integral Points In A Polyhedral Region

Author : Anonim
Publisher : Unknown
Page : 652 pages
File Size : 47,5 Mb
Release : 1975
Category : Military research
ISBN : PURD:32754077760753

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Research in Progress by Anonim Pdf

Author : Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 48,5 Mb
Release : 2006-06-22
Category : Business & Economics
ISBN : 9780387236391

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Generalized Convexity, Generalized Monotonicity and Applications by Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc Pdf

In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.

Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory,Gary A. Kochman
Publisher : Unknown
Page : 166 pages
File Size : 44,6 Mb
Release : 1976
Category : Algorithms
ISBN : STANFORD:36105046361320

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Decomposition in Integer Programming by Stanford University. Department of Operations Research. Systems Optimization Laboratory,Gary A. Kochman Pdf

Contents: Resource Decomposition: A Conceptual Outline; Branching in the Rudimentary Branch-and-Bound Algorithm; Computing Bounds: Single Linking Constraint Case; Computing Bounds: Multiple Linking Constraints Case; Computational Results; and Conclusions, Extensions, and Areas for Future Research.

Author : Anonim
Publisher : Unknown
Page : 1016 pages
File Size : 42,7 Mb
Release : 1985
Category : Government reports announcements & index
ISBN : MINN:30000008704417

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Government Reports Annual Index by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1262 pages
File Size : 45,9 Mb
Release : 1975
Category : Government publications
ISBN : MINN:31951000848736G

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Government Reports Index by Anonim Pdf

Author : Stanford University. Institute for Energy Studies
Publisher : Unknown
Page : 94 pages
File Size : 46,9 Mb
Release : 1980
Category : Electronic
ISBN : STANFORD:36105046332453

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Status of Energy Policy Research at Stanford by Stanford University. Institute for Energy Studies Pdf

Author : Anonim
Publisher : Unknown
Page : 540 pages
File Size : 47,7 Mb
Release : 1976
Category : Industrial management
ISBN : UOM:39015011163659

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Management Science by Anonim Pdf

Includes special issues: The Professional series in the management sciences.

Author : Anonim
Publisher : Unknown
Page : 1210 pages
File Size : 40,8 Mb
Release : 1974
Category : Technology
ISBN : MINN:31951000848718I

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Government Reports Announcements by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1208 pages
File Size : 55,7 Mb
Release : 1974
Category : Science
ISBN : UIUC:30112075615473

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Government Reports Announcements & Index by Anonim Pdf

Author : Christian Wagner
Publisher : Cuvillier Verlag
Page : 181 pages
File Size : 47,5 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9783736939271

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Maximal Lattice-Free Polyhedra in Mixed-Integer Cutting Plane Theory by Christian Wagner Pdf

This thesis deals with the generation, evaluation, and analysis of cutting planes for mixed-integer linear programs (MILP's). Such optimization problems involve finitely many variables, some of which are required to be integer. The aim is to maximize or minimize a linear objective function over a set of finitely many linear equations and inequalities. Many industrial problems can be formulated as MILP's. The presence of both, discrete and continuous variables, makes it difficult to solve MILP's algorithmically. The currently available algorithms fail to solve many real-life problems in acceptable time or can only provide heuristic solutions. As a consequence, there is an ongoing interest in novel solution techniques. A standard approach to solve MILP's is to apply cutting plane methods. Here, the underlying MILP is used to construct a sequence of linear programs whose formulations are improved by successively adding linear constraints – so-called cutting planes – until one of the linear programs has an optimal solution which satisfies the integrality conditions on the integer constrained variables. For many combinatorial problems, it is possible to immediately deduce several families of cutting planes by exploiting the inherent combinatorial structure of the problem. However, for general MILP's, no structural properties can be used. The generation of cutting planes must rather be based on the objective function and the given, unstructured set of linear equations and inequalities. On the one hand, this makes the derivation of strong cutting planes for general MILP's more difficult than the derivation of cutting planes for structured problems. On the other hand, for this very reason, the analysis of cutting plane generation for general MILP's becomes mathematically interesting. This thesis presents an approach to generate cutting planes for a general MILP. The cutting planes are obtained from lattice-free polyhedra, that is polyhedra without interior integer point. The point of departure is an optimal solution of the linear programming relaxation of the underlying MILP. By considering multiple rows of an associated simplex tableau, a further relaxation is derived. The first part of this thesis is dedicated to the analysis of this relaxation and it is shown how cutting planes for the general MILP can be deduced from the considered relaxation. It turns out that the generated cutting planes have a geometric interpretation in the space of the discrete variables. In particular, it is shown that the strongest cutting planes which can be derived from the considered relaxation correspond to maximal lattice-free polyhedra. As a result, problems on cutting planes are transferable into problems on maximal lattice-free polyhedra. The second part of this thesis addresses the evaluation of the generated cutting planes. It is shown that the cutting planes which are important, are at the same time the cutting planes which are difficult to derive in the sense that they correspond to highly complex maximal lattice-free polyhedra. In addition, it is shown that under certain assumptions on the underlying system of linear equations and inequalities, the important cutting planes can be approximated with cutting planes which correspond to less complex maximal lattice-free polyhedra. A probabilistic model is used to complement the analysis. Moreover, a geometric interpretation of the results is given. The third part of this thesis focuses on the analysis of lattice-free polyhedra. In particular, the class of lattice-free integral polyhedra is investigated, a class which is important within a cutting plane framework. Two different notions of maximality are introduced. It is distinguished into the class of lattice-free integral polyhedra which are not properly contained in another lattice-free integral polyhedron, and the class of lattice-free integral polyhedra which are not properly contained in another lattice-free convex set. Both classes are analyzed, especially with respect to the properties of their representatives and the relation between the two classes. It is shown that both classes are of large cardinality and that they contain very large elements. For the second as well as the third part of this thesis, statements about two-dimensional lattice-free convex sets are needed. For that reason, the fourth part of this thesis is devoted to the derivation of these results.

Author : Dino Ahr,Roland Fahrion,Marcus Oswald,Gerhard Reinelt
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642170225

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Operations Research Proceedings 2003 by Dino Ahr,Roland Fahrion,Marcus Oswald,Gerhard Reinelt Pdf

This volume contains a selection of papers referring to lectures presented at the symposium "Operations Research 2003" (OR03) held at the Ruprecht Karls-Universitiit Heidelberg, September 3 - 5, 2003. This international con ference took place under the auspices of the German Operations Research So ciety (GOR) and of Dr. Erwin Teufel, prime minister of Baden-Wurttemberg. The symposium had about 500 participants from countries all over the world. It attracted academians and practitioners working in various field of Opera tions Research and provided them with the most recent advances in Opera tions Research and related areas in Economics, Mathematics, and Computer Science. The program consisted of 4 plenary and 13 semi-plenary talks and more than 300 contributed papers selected by the program committee to be presented in 17 sections. Due to a limited number of pages available for the proceedings volume, the length of each article as well as the total number of accepted contributions had to be restricted. Submitted manuscripts have therefore been reviewed and 62 of them have been selected for publication. This refereeing procedure has been strongly supported by the section chairmen and we would like to express our gratitude to them. Finally, we also would like to thank Dr. Werner Muller from Springer-Verlag for his support in publishing this proceedings volume.

Author : Krzysztof Galkowski,Jeff David Wood
Publisher : CRC Press
Page : 284 pages
File Size : 55,8 Mb
Release : 2001-05-10
Category : Technology & Engineering
ISBN : 0203303407

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Multidimensional Signals, Circuits and Systems by Krzysztof Galkowski,Jeff David Wood Pdf

Although research on general multidimensional systems theory has been developing rapidly in recent years, this is the first research text to appear on the subject since the early 1980s. The text describes the current state of the art nD systems and sets out a number of open problems, and gives several different perspectives on the subject. It presents a number of different solutions to major theoretical problems as well as some interesting practical results. The book comprises of a selection of plenary and other lectures given at The First International Workshop on Multidimensional (nD) Systems (NDS-98) held in 1998 in Poland, and is written by leading world specialists in the field.

Author : Matthias Beck,Sinai Robins
Publisher : Springer
Page : 285 pages
File Size : 45,7 Mb
Release : 2015-11-14
Category : Mathematics
ISBN : 9781493929696

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Computing the Continuous Discretely by Matthias Beck,Sinai Robins Pdf

This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

Author : Alexander Barvinok
Publisher : European Mathematical Society
Page : 204 pages
File Size : 53,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190523

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Integer Points in Polyhedra by Alexander Barvinok Pdf

This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra-Lenstra-Lovasz lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.

Author : Anonim
Publisher : Unknown
Page : 1166 pages
File Size : 41,6 Mb
Release : 1967
Category : Science
ISBN : WISC:89094802246

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U.S. Government Research & Development Reports by Anonim Pdf