Duality In Discrete Programming Ii The Quadratic Case PDF Download
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Author | : Egon Balas |
Publisher | : |
Total Pages | : 14 |
Release | : 1967 |
Genre | : |
ISBN | : |
Download Duality in Discrete Programming: Ii. the Quadratic Case Book in PDF, ePub and Kindle
The paper extends the results of 'Duality in Discrete Programming' (1) to the case of quadratic objective functions. The paper is, however, self-contained. A pair of symmetric dual quadratic programs is generalized by constraining some of the variables to belong to arbitrary sets of real numbers. Quadratic all-integer and mixed-integer programs are special cases of these problems. The resulting primal problem is shown, subject to a qualification, to have an optimal solution if and only if the dual has one, and in this case the values of their respective objective functions are equal. Most of the other results of (1) are also shown to carry over to the quadratic case. (Author).
Author | : William S. Dorn |
Publisher | : |
Total Pages | : 26 |
Release | : 1958 |
Genre | : Duality (Nuclear physics) |
ISBN | : |
Download Duality in Quadratic Programming Book in PDF, ePub and Kindle
Author | : C. Kastning |
Publisher | : Springer Science & Business Media |
Total Pages | : 504 |
Release | : 2013-11-11 |
Genre | : Business & Economics |
ISBN | : 3662022842 |
Download Integer Programming and Related Areas Book in PDF, ePub and Kindle
Integer Prograw~ing is one of the most fascinating and difficult areas in the field of Mathematical Optimization. Due to this fact notable research contributions to Integer Programming have been made in very different branches of mathematics and its applications. Since these publications are scattered over many journals, proceedings volumes, monographs, and working papers, a comprehensive bibliography of all these sources is a helpful tool even for specialists in this field. I initiated this compilation of literature in 1970 at the Institut fur ~konometrie und Operations Research, University of Bonn. Since then many collaborators have contributed to and worked on it. Among them Dipl.-Math. Claus Kastning has done the bulk of the work. With great perseverance and diligence he has gathered all the material and checked it with the original sources. The main aim was to incorporate rare and not easily accessible sources like Russian journals, preprints or unpublished papers. Without the invaluable and dedicated engagement of Claus Kastning the bibliography would never have reached this final version. For this reason he must be considered its responsible editor. As with any other collection this literature list has a subjective viewpoint and may be in some sense incomplete. We have however tried to be as complete as possible. The bibliography contains 4704 different publications by 6767 authors which were classified by 11839 descriptor entries.
Author | : Hamdy A. Taha |
Publisher | : Academic Press |
Total Pages | : 395 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483260372 |
Download Integer Programming Book in PDF, ePub and Kindle
Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming. Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other chapters consider the branch-and-bound methods, the cutting-plane method, and its closely related asymptotic problem. This book discusses as well several specialized algorithms for certain well-known integer models and provides an alternative approach to the solution of the integer problem. The final chapter deals with a number of observations about the formulations and executions of integer programming models. This book is a valuable resource for industrial engineers and research workers.
Author | : |
Publisher | : Elsevier |
Total Pages | : 571 |
Release | : 2011-10-10 |
Genre | : Mathematics |
ISBN | : 0080867642 |
Download Studies in Integer Programming Book in PDF, ePub and Kindle
Studies in Integer Programming
Author | : Josef Stoer |
Publisher | : Springer Science & Business Media |
Total Pages | : 306 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642462162 |
Download Convexity and Optimization in Finite Dimensions I Book in PDF, ePub and Kindle
Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back ground for the arithmetic of convex optimization to be treated in a sub sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.
Author | : |
Publisher | : Elsevier |
Total Pages | : 461 |
Release | : 2000-04-01 |
Genre | : Mathematics |
ISBN | : 0080867677 |
Download Discrete Optimization I Book in PDF, ePub and Kindle
Discrete Optimization I
Author | : Harvey M. Salkin |
Publisher | : North Holland |
Total Pages | : 788 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : |
Download Foundations of Integer Programming Book in PDF, ePub and Kindle
Author | : Egon Balas |
Publisher | : |
Total Pages | : 36 |
Release | : 1968 |
Genre | : Integer programming |
ISBN | : |
Download Duality in discrete programming Book in PDF, ePub and Kindle
A duality theory is proposed for discrete programming. The mixed-integer programming problem is shown to be a special case of a minimax problem with a Lagrangian-type objective function, linear constraints, and some variables constrained to belong to an arbitrary set of real numbers. The dual of this problem is formulated as a problem of the same type, and such that the dual of the dual is the primal. It is shown that the primal has an optimal solution if and only if the dual has one, and in this case the values of their respective objective functions are equal. An optimal solution to the primal and the dual is shown to have the saddle-point property of optimal solutions to a pair of dual linear (and certain nonlinear) programs. A certain type of complementary slackness is shown to hold. Conditions for the uniqueness of a solution are examined. Finally, an economic interpretation is outlined in terms of a generalized shadow-prince system for mixed-integer programs.
Author | : Harvey M. Salkin |
Publisher | : Addison Wesley Publishing Company |
Total Pages | : 566 |
Release | : 1975 |
Genre | : Mathematics |
ISBN | : |
Download Integer Programming Book in PDF, ePub and Kindle