Download or read book Duality in Discrete Programming Ii the Quadratic Case written by Egon Balas and published by . This book was released on 1967 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Duality in Quadratic Programming written by William S. Dorn and published by . This book was released on 1958 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer Programming and Related Areas written by C. Kastning and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 The main aim was to incorporate rare and not easily accessible sources like Russian journals, preprints or unpublished papers.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.
Download or read book Integer Programming written by Hamdy A. Taha and published by Academic Press. This book was released on 2014-05-10 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Studies in Integer Programming written by and published by Elsevier. This book was released on 2011-10-10 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Integer Programming
Download or read book Convexity and Optimization in Finite Dimensions I written by Josef Stoer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Discrete Optimization I written by and published by Elsevier. This book was released on 2000-04-01 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Optimization I
Download or read book Foundations of Integer Programming written by Harvey M. Salkin and published by North Holland. This book was released on 1989 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Duality in discrete programming written by Egon Balas and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Encyclopedia of Computer Science and Technology written by Jack Belzer and published by CRC Press. This book was released on 1975-09-01 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This comprehensive reference work provides immediate, fingertip access to state-of-the-art technology in nearly 700 self-contained articles written by over 900 international authorities. Each article in the Encyclopedia features current developments and trends in computers, software, vendors, and applications...extensive bibliographies of leading figures in the field, such as Samuel Alexander, John von Neumann, and Norbert Wiener...and in-depth analysis of future directions."
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer Programming written by Robert Garfinkel and published by Wiley-Interscience. This book was released on 1972 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear programming; Integer programming graphs; Enumeration methods; Cutting plane methods; The knapsack problem; Integer programming over cones; The set covering and partitioning problems; Approximate methods; Integer nonlinear programming; Computational experience.
Download or read book Mathematical Programming Study written by and published by . This book was released on 1980 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer Programming written by Harvey M. Salkin and published by Addison Wesley Publishing Company. This book was released on 1975 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Management Science written by and published by . This book was released on 1986 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues for Feb. 1965-Aug. 1967 include Bulletin of the Institute of Management Sciences.
Download or read book U S Government Research Development Reports written by and published by . This book was released on 1969-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canonical Duality Theory written by David Yang Gao and published by Springer. This book was released on 2017-10-09 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
