Download or read book Geometric Programming Duality in Quadratic Programming and Lp approximation written by Elmor L. Peterson and published by . This book was released on 1968 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The duality theory of geometric programming as developed by Duffin, Peterson and Zener is based on abstract properties shared by certain classical inequalities, such as Cauchy's arithmetic-geometric mean inequality and Holder's inequality. Inequalities with these abstract properties have been termed 'geometric inequalities.' In this paper we establish a new geometric inequality and use it to extend the 'refined duality theory' for 'posynomial' geometric programs. This extended duality theory treats both 'quadratically-constrained quadratic programs' and 'l sub p-constrained l sub p-approximation (regression) problems' through a rather novel and unified formulation of these two classes of programs. This work generalizes some of the work of others on linearly-constrained quadratic programs, and provides to the best of our knowledge the first explicit formulation of duality for constrained approximation problems. Other people have developed duality theories for a larger class of programs, namely all convex programs, but those theories (when applied to the programs considered here) are not nearly as strong as the theory developed here. This theory has virtually all of the desirable features of its analog for posynomial programs, and its proof provides useful computational procedures. (Author).
Download or read book GEOMETRIC PROGRAMMING DUALITY IN QUADRATIC PROGRAMMING AND LP APPROXIMATION III DEGENERATE PROGRAMS written by UNITED STATES. DEPARTMENT OF THE ARMY. MATHEMATICS RESEARCH CENTER. and published by . This book was released on with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book GEOMETRIC PROGRAMMING DUALITY IN QUADRATIC PROGRAMMING AND L P APPROXIMATION written by JOSEPH GEORGE ECKER and published by . This book was released on 1968 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Programming written by Elmor L. Peterson and published by . This book was released on 1969 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 GEOMETRIC PROGRAMMING DUALITY IN QUADRATIC PROGRAMMING AND L Sub P APPROXIMATION III DEGENERATE PROGRAMS written by Elmor L. Peterson and published by . This book was released on 1969 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Degenerate quadratically-constrained quadratic programs and l sub p-constrained l sub p-approximation problems are defined and investigates within the framework of extended geometric programming. (Author).
Download or read book Geometric Programming for Communication Systems written by Mung Chiang and published by Now Publishers Inc. This book was released on 2005 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols. Geometric Programming for Communication Systems begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results. Geometric Programming for Communication Systems is intended for researchers and students who wish to have a comprehensive starting point for understanding the theory and applications of geometric programming in communication systems.
Download or read book Advances in Geometric Programming written by Mordecai Avriel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1961, C. Zener, then Director of Science at Westinghouse Corpora tion, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathe matical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from Carnegie Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes tingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory.
Download or read book Handbook of Semidefinite Programming written by Henry Wolkowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook of Semidefinite Programming offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.
Download or read book Nonlinear Programming written by J. B. Rosen and published by Elsevier. This book was released on 2014-05-10 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Programming contains the proceedings of a Symposium on Nonlinear Programming held in Madison, Wisconsin on May 4-6, 1970. This book emphasizes algorithms and related theories that lead to efficient computational methods for solving nonlinear programming problems. This compilation consists of 17 chapters. Chapters 1 to 9 are concerned primarily with computational algorithms, while Chapters 10 to 13 are devoted to theoretical aspects of nonlinear programming. Certain applications of nonlinear programming are considered in Chapters 14 to 17. The algorithms for nonlinear constraint problems, investigation of convergence rates, and use of nonlinear programming for approximation are also covered in this text. This publication is a good source for students and researchers concerned with nonlinear programming.
Download or read book Proceedings of the Princeton Symposium on Mathematical Programming written by Harold William Kuhn and published by Princeton University Press. This book was released on 2015-03-08 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Naval Research Logistics Quarterly written by and published by . This book was released on 1971 with total page 1396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Geometric Programming written by Charles S. Beightler and published by John Wiley & Sons. This book was released on 1976 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constrained optimization problems: basic concepts; Posynomial geometric programming; Practical aspect of G.P. problem-solving; Signomial geometric programming; Tactics for handling posynomial programs with loose constraints and degreess of difficulty; Extensions of geometric programming to non-standard forms; Reversed constraints and transformations to posynomial programs; Solutions of signomial programs through condensation; The underlying primal structure and its use in computation; Selected applications of geometric programming;
Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Download or read book Research in Progress written by and published by . This book was released on 1967 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Methods for Quadratic Programming written by Yves Dominique Brise and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This PhD thesis was written at ETH Zurich, in Prof. Dr. Emo Welzl's research group, under the supervision of Dr. Bernd Garnter. It shows two theoretical results that are both related to quadratic programming. The first one concerns the abstract optimization framework of violator spaces and the randomized procedure called Clarkson's algorithm. In a nutshell, the algorithm randomly samples from a set of constraints, computes an optimal solution subject to these constraints, and then checks whether the ignored constraints violate the solution. If not, some form of re-sampling occurs. We present the algorithm in the easiest version that can still be analyzed successfully. The second contribution concerns quadratic programming more directly. It is well-known that a simplex-like procedure can be applied to quadratic programming. The main computational effort in this algorithm comes from solving a series of linear equation systems that change gradually. We develop the integral LU decomposition of matrices, which allows us to solve the equation systems efficiently and to exploit sparse inputs. Last but not least, a considerable portion of the work included in this thesis was devoted to implementing the integral LU decomposition in the framework of the existing quadratic programming solver in the Computational Geometry Algorithms Library (CGAL). In the last two chapters we describe our implementation and the experimental results we obtained.
Download or read book Lectures on Modern Convex Optimization written by Aharon Ben-Tal and published by SIAM. This book was released on 2001-01-01 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
