A Note on the Dual of an Unconstrained (Generalized) Geometric Programming Problem PDF Download
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Author: J. B. G. Frenk
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In this note we show that the strong duality theorem of an unconstrained (generalized) geometric programming problem as defined by Peterson (cf.[1]) is actually a special case of a Lagrangian duality result. Contrary to [1] we also consider the case that the set C is compact and convex and in this case we do not need to assume the standard regularity condition.
Author: J. B. G. Frenk
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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In this note we show that the strong duality theorem of an unconstrained (generalized) geometric programming problem as defined by Peterson (cf.[1]) is actually a special case of a Lagrangian duality result. Contrary to [1] we also consider the case that the set C is compact and convex and in this case we do not need to assume the standard regularity condition.
Author: J. B. G. Frenk
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Author: Elmor L. Peterson
Publisher:
ISBN:
Category : Geometric programming
Languages : en
Pages : 83
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The conjugate transform is used to generalize, symmetrize, and further study Duffin's original formulation of duality for unconstrained geometric programming. This study provides new economic interpretations for the geometric dual problem; and it yields new theorems concerning the existence, uniqueness, and characterization of optimal solutions. The economic interpretations come from a new closed-form solution to a related economically interesting class of convex programming problems. (Author).
Author: Mordecai Avriel
Publisher: Springer Science & Business Media
ISBN: 1461582857
Category : Mathematics
Languages : en
Pages : 457
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Book Description
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.
Author: Mung Chiang
Publisher: Now Publishers Inc
ISBN: 9781933019093
Category : Computers
Languages : en
Pages : 172
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Book Description
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.
Author:
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ISBN:
Category : Logistics, Naval
Languages : en
Pages : 1396
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Author: Patrick Brockett
Publisher:
ISBN:
Category : Decision making
Languages : en
Pages : 11
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This document formulates the generalized constrained maximum entropy problem often used in a decision making context as an extended dual convex programming problem. The dual problem is then presented. In this dual setting the primal Lagrange multipliers are precisely the dual variables, and are easily calculated directly by virtue of the simple structure of the dual problem. An example involving the selection of best equipment for an oil spill is presented as an illustration. The authors contrast their solution with those given by previous authors. (Author).
Author: Stephen P. Boyd
Publisher: Cambridge University Press
ISBN: 9780521833783
Category : Business & Economics
Languages : en
Pages : 744
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Book Description
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.
Author: Carlton Scott
Publisher:
ISBN:
Category : Geometric programming
Languages : en
Pages : 240
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Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 932
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