Advances In Geometric Programming
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Advances In Geometric Programming
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Author : Mordecai Avriel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Advances In Geometric Programming written by Mordecai Avriel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Advances In Geometric Modeling And Processing
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Author : Falai Chen
language : en
Publisher: Springer
Release Date : 2008-04-30
Advances In Geometric Modeling And Processing written by Falai Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-30 with Computers categories.
GeometricModelingandProcessing(GMP)isabiennialinternationalconference on geometric modeling, simulation and computing, which provides researchers and practitioners with a forum for exchanging new ideas, discussing new app- cations, and presenting new solutions. Previous GMP conferences were held in Pittsburgh (2006), Beijing (2004), Tokyo (2002), and Hong Kong (2000). This, the 5th GMP conference, was held in Hangzhou, one of the most beautiful cities in China. GMP 2008 received 113 paper submissions, covering a wide spectrum of - ometric modeling and processing, such as curves and surfaces, digital geometry processing, geometric feature modeling and recognition, geometric constraint solving, geometric optimization, multiresolution modeling, and applications in computer vision, image processing, scienti?c visualization, robotics and reverse engineering. Each paper was reviewed by at least three members of the program committee andexternalreviewers.Basedonthe recommendations ofthe revi- ers, 34 regular papers were selected for oral presentation, and 17 short papers were selected for poster presentation. All selected papers are included in these proceedings. We thank all authors, external reviewers and program committee members for their great e?ort and contributions, which made this conference a success.
Applied Geometric Programming
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Author : Charles S. Beightler
language : en
Publisher: John Wiley & Sons
Release Date : 1976
Applied Geometric Programming written by Charles S. Beightler and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
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;
Fuzzy Geometric Programming Techniques And Applications
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Author : Sahidul Islam
language : en
Publisher: Springer
Release Date : 2019-01-31
Fuzzy Geometric Programming Techniques And Applications written by Sahidul Islam and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-31 with Business & Economics categories.
This book develops the concepts of various unique optimization techniques in the crisp and fuzzy environment. It provides an extensive overview of geometric programming methods within a unifying framework, and presents an in-depth discussion of the modified geometric programming problem, fuzzy geometric programming, as well as new insights into goal geometric programming. With numerous examples and exercises together with detailed solutions for several problems, the book also addresses fuzzy multi-objective geometric programming techniques. Geometric programming, which falls into the general class of signomial problems, has applications across disciplines, from engineering to economics, and is extremely useful in applications of a variety of optimization problems. Organized into thirteen chapters, this book is a valuable resource for graduate and advanced undergraduate students and researchers in applied mathematics and engineering.
Geometric Programming For Design Equation Development And Cost Profit Optimization With Illustrative Case Study Problems And Solutions Third Edition
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Author : Robert Creese
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Geometric Programming For Design Equation Development And Cost Profit Optimization With Illustrative Case Study Problems And Solutions Third Edition written by Robert Creese and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
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.
Geometric Programming For Design And Cost Optimization 2nd Edition
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Author : Robert Creese
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Geometric Programming For Design And Cost Optimization 2nd Edition written by Robert Creese and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
Geometric programming is used for design and cost optimization, the development of generalized design relationships, cost ratios for specific problems, and profit maximization. The early pioneers of the process - Zener, Duffin, Peterson, Beightler, Wilde, and Phillips -- played important roles in the development of geometric programming. There are three major areas: 1) Introduction, History, and Theoretical Fundamentals, 2) Applications with Zero Degrees of Difficulty, and 3) Applications with Positive Degrees of Difficulty. The primal-dual relationships are used to illustrate how to determine the primal variables from the dual solution and how to determine additional dual equations when the degrees of difficulty are positive. A new technique for determining additional equations for the dual, Dimensional Analysis, is demonstrated. The various solution techniques of the constrained derivative approach, the condensation of terms, and dimensional analysis are illustrated with example problems. The goal of this work is to have readers develop more case studies to further the application of this exciting tool. Table of Contents: Introduction / Brief History of Geometric Programming / Theoretical Considerations / The Optimal Box Design Case Study / Trash Can Case Study / The Open Cargo Shipping Box Case Study / Metal Casting Cylindrical Riser Case Study / Inventory Model Case Study / Process Furnace Design Case Study / Gas Transmission Pipeline Case Study / Profit Maximization Case Study / Material Removal/Metal Cutting Economics Case Study / Journal Bearing Design Case Study / Metal Casting Hemispherical Top Cylindrical Side Riser\\Case Study / Liquefied Petroleum Gas (LPG) Cylinders Case Study / Material Removal/Metal Cutting Economics with Two Constraints / The Open Cargo Shipping Box with Skids / Profit Maximization Considering Decreasing Cost Functions of Inventory Policy / Summary and Future Directions / Thesis and Dissertations on Geometric Programming
Geometric Programming For Design Equation Development And Cost Profit Optimization
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Author : Robert C. Creese
language : en
Publisher: Morgan & Claypool
Release Date : 2016-12-27
Geometric Programming For Design Equation Development And Cost Profit Optimization written by Robert C. Creese and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with Technology & Engineering categories.
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.
Geometric Programming For Communication Systems
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Author : Mung Chiang
language : en
Publisher: Now Publishers Inc
Release Date : 2005
Geometric Programming For Communication Systems written by Mung Chiang and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
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.
Robust Design Via Geometric And Signomial Programming
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Author : Ali Saab
language : en
Publisher:
Release Date : 2018
Robust Design Via Geometric And Signomial Programming written by Ali Saab and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Solving convex optimization problems has become extremely efficient and reliable after the recent development of polynomial-time algorithms and advancement in computing power. Geometric Programming (GP) and Signomial Programming (SP) has been proven successful in optimizing multidisciplinary designs due to exploiting the speed of convergence and the ability to model non-linear designs. However, an optimal solution of GPs and SPs can be sensitive to uncertainties in the parameters involved in the problem. In fact, robust optimization can incorporate the uncertainties in an optimization problem and solves for the worst-case scenario. Yet, robust geometric programs (RGPs) and robust signomial programs (RSPs) are not known to have a tractable formulation that current solvers can efficiently solve. In this thesis, approximate formulations of RGPs and RSPs are proposed. Recently, the curiosity regarding the deployment of GPs and SPs in model complex engineering systems has been growing. This awareness has motivated modeling the uncertainties that are fundamental to engineering design optimization. Consequently, RGPs and RSPs provide a framework for modeling and solving GPs and SPs while representing their ambiguities as belonging to an uncertainty set. The RGP methodologies presented here are based on reformulating the GP as a convex program and then robustifying it with methods from robust linear programming. The RSP methodology is based on solving sequential local RGP approximations. These new methodologies, along with previous ones from the literature, are used to robustify aircraft design problems, and the results of these different methodologies are compared and discussed.
Geometric Programming For Design And Cost Optimization
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Author : Robert Creese
language : en
Publisher: Springer Nature
Release Date : 2009-10-11
Geometric Programming For Design And Cost Optimization written by Robert Creese and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-11 with Technology & Engineering categories.
Geometric programming is used for design and cost optimization and the development of generalized design relationships and cost rations for specific problems. The early pioneers of the process, Zener, Duffin, Peterson, Beightler, and Wilde, played important roles in the development of geometric programming. The theory of geometric programming is presented and 10 examples are presented and solved in detail. The examples illustrate some of the difficulties encountered in typical problems and techniques for overcoming these difficulties. The primal-dual relationships are used to illustrate how to determine the primal variables from the dual solution. These primal-dual relationships can be used to determine additional dual equations when the degrees of difficulty are positive. The goal of this work is to have readers develop more case studies to further the application of this exciting mathematical tool. Table of Contents: Introduction / Brief History of Geometric Programming / Theoretical Considerations / Trash Can Case Study / Open Cargo Shipping Box Case Study / Metal Casting Cylindrical Riser Case Study / Process Furnace Design Case Study / Gas Transmission Pipeline Case Study / Journal Bearing Design Case Study / Metal Casting Hemispherical Top Cylindrical Side Riser / Liquefied Petroleum Gas(LPG) Cylinders Case Study / Material Removal/Metal Cutting Economics Case Study / Summary and Future Directions