Geometric Programming for Communication Systems
Geometric Programming for Communication Systems

Author: Mung Chiang

Publisher: Now Publishers Inc

Published: 2005

Total Pages: 172

ISBN-13: 9781933019093

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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results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results.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.

Geometric Programming for Design Equation Development and Cost/Profit Optimization (with illustrative case study problems and solutions), Third Edition
Geometric Programming for Design Equation Development and Cost/Profit Optimization (with illustrative case study problems and solutions), Third Edition

Author: Robert Creese

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 194

ISBN-13: 3031793765

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Geometric Programming is used for cost minimization, profit maximization, obtaining cost ratios, and the development of generalized design equations for the primal variables. The early pioneers of geometric programming—Zener, Duffin, Peterson, Beightler, Wilde, and Phillips—played important roles in its development. Five new case studies have been added to the third edition. There are five major sections: (1) Introduction, History and Theoretical Fundamentals; (2) Cost Minimization Applications with Zero Degrees of Difficulty; (3) Profit Maximization Applications with Zero Degrees of Difficulty; (4) Applications with Positive Degrees of Difficulty; and (5) Summary, Future Directions, and Geometric Programming Theses & Dissertations Titles. The various solution techniques presented are the constrained derivative approach, condensation of terms approach, dimensional analysis approach, and transformed dual approach. A primary goal of this work is to have readers develop more case studies and new solution techniques to further the application of geometric programming.

Canonical Duality Theory
Canonical Duality Theory

Author: David Yang Gao

Publisher: Springer

Published: 2017-10-09

Total Pages: 374

ISBN-13: 3319580175

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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.

The Application of Generalized Geometric Programming (Conjugate Duality) to the Analysis and Solution of Convex Programs
The Application of Generalized Geometric Programming (Conjugate Duality) to the Analysis and Solution of Convex Programs

Author: Thomas R. Jefferson

Publisher:

Published: 1985

Total Pages: 10

ISBN-13:

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The research in this grant involves the application of generalized geometric programming (conjugate duality) to a variety of problems. The duality theory constructs a dual program which can provide insight into the problem and assist in solution. Composite geometric programming was developed as an important new class of mathematical programming was developed as an important new class of mathematical programs. Applications studied included machining economics, resource allocation, assignment, nonlinear multicommodity network flow problems, mineral processing, statistical analysis of ordinal categorical data, and estimation. Geometric programming was extended from functions of posynomial form to functions which include exponential, logarithmic and other factors by the development of composite geometric programming. This class retains the power of geometric programming while addressing new problems. Certain machining economics problems and chemical equilibrium problems fall into this new class of mathematical programs. Research on the machining economics problem resulted in the problem being reduced from a nonlinear program to a one-dimensional search. In addition, duality theory provided easy parametric analysis.

Advances in Applied Mathematics and Global Optimization
Advances in Applied Mathematics and Global Optimization

Author: David Y. Gao

Publisher: Springer Science & Business Media

Published: 2009-04-09

Total Pages: 542

ISBN-13: 0387757147

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The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.