Principles of Optimization Theory

Author: C. R. Bector
Publisher: Alpha Science International, Limited
ISBN: UOM:39015060898023
Release Date: 2005
Genre: Mathematics

An account of the fundamental principles of optimization theory blended in a judicious way with current research. It helps the reader to probe into such advanced topics like Non-smooth Optimization and Conjugate Duality.

Optimization Theory with Applications

Author: Donald A. Pierre
Publisher: Courier Corporation
ISBN: 9780486136950
Release Date: 2012-07-12
Genre: Mathematics

Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.

Foundations of Optimization

Author: Osman Güler
Publisher: Springer Science & Business Media
ISBN: 0387684077
Release Date: 2010-08-03
Genre: Business & Economics

This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.

A First Course in Optimization Theory

Author: Rangarajan K. Sundaram
Publisher: Cambridge University Press
ISBN: 0521497701
Release Date: 1996-06-13
Genre: Business & Economics

Divided into three separate parts, this book introduces students to optimization theory and its use in economics and allied disciplines. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

Optimization in Economic Theory

Author: Avinash K. Dixit
Publisher: Oxford University Press on Demand
ISBN: 0198772106
Release Date: 1990
Genre: Business & Economics

Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and reviews functions defined by solutions of optimization problems. Recently revised and expanded, the second edition will be a valuable resource for upper level undergraduate and graduate students.

Practical Mathematical Optimization

Author: Jan Snyman
Publisher: Springer Science & Business Media
ISBN: 9780387243498
Release Date: 2005-12-15
Genre: Mathematics

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

Algorithmic Principles of Mathematical Programming

Author: Ulrich Faigle
Publisher: Springer Science & Business Media
ISBN: 9789401598965
Release Date: 2013-04-17
Genre: Mathematics

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

Duality Principles in Nonconvex Systems

Author: David Yang Gao
Publisher: Springer Science & Business Media
ISBN: 9781475731767
Release Date: 2013-03-09
Genre: Mathematics

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Engineering Optimization

Author: Singiresu S. Rao
Publisher: John Wiley & Sons
ISBN: 9780470183526
Release Date: 2009-07-20
Genre: Mathematics

Technology/Engineering/Mechanical Helps you move from theory to optimizing engineering systems in almost any industry Now in its Fourth Edition, Professor Singiresu Rao's acclaimed text Engineering Optimization enables readers to quickly master and apply all the important optimization methods in use today across a broad range of industries. Covering both the latest and classical optimization methods, the text starts off with the basics and then progressively builds to advanced principles and applications. This comprehensive text covers nonlinear, linear, geometric, dynamic, and stochastic programming techniques as well as more specialized methods such as multiobjective, genetic algorithms, simulated annealing, neural networks, particle swarm optimization, ant colony optimization, and fuzzy optimization. Each method is presented in clear, straightforward language, making even the more sophisticated techniques easy to grasp. Moreover, the author provides: Case examples that show how each method is applied to solve real-world problems across a variety of industries Review questions and problems at the end of each chapter to engage readers in applying their newfound skills and knowledge Examples that demonstrate the use of MATLAB® for the solution of different types of practical optimization problems References and bibliography at the end of each chapter for exploring topics in greater depth Answers to Review Questions available on the author's Web site to help readers to test their understanding of the basic concepts With its emphasis on problem-solving and applications, Engineering Optimization is ideal for upper-level undergraduates and graduate students in mechanical, civil, electrical, chemical, and aerospace engineering. In addition, the text helps practicing engineers in almost any industry design improved, more efficient systems at less cost.

Optimization of Tax Sovereignty and Free Movement

Author: Sjoerd Douma
Publisher: IBFD
ISBN: 9789087221126
Release Date: 2011
Genre: Direct taxation

The book argues that the notions of tax sovereignty and EU free movement should be regarded as two fundamentally equal principles. The conflict between these two principles is resolved by establishing, in individual cases, the optimum position between two extremes: a general unrestricted freedom of action by states versus a prohibition of any obstacle to the free movement of goods, persons, services and capital. The process of reconciliation of these competing principles is structured by the theoretical optimization model developed in the present study. This model is external to the present case law. The application of the theoretical optimization model to the ECJ’s case law in the area of direct taxation reveals that this case law is largely in line with the model. It is certainly not as internally inconsistent as claimed in some of the tax literature. Many jigsaw pieces seem to fit after all if the case law is assessed in the light of the model. A number of future developments could be expected on the basis of the model and extensive case law analysis. The most important of these is that, in some cases, truly non-discriminatory tax measures should give rise to a prima facie restriction on free movement.

Principles of Optimal Design

Author: Panos Y. Papalambros
Publisher: Cambridge University Press
ISBN: 9781316867457
Release Date: 2017-01-09
Genre: Technology & Engineering

Design optimization is a standard concept in engineering design, and in other disciplines which utilize mathematical decision-making methods. This textbook focuses on the close relationship between a design problem's mathematical model and the solution-driven methods which optimize it. Along with extensive material on modeling problems, this book also features useful techniques for checking whether a model is suitable for computational treatment. Throughout, key concepts are discussed in the context of why and when a particular algorithm may be successful, and a large number of examples demonstrate the theory or method right after it is presented. This book also contains step-by-step instructions for executing a design optimization project - from building the problem statement to interpreting the computer results. All chapters contain exercises from which instructors can easily build quizzes, and a chapter on 'principles and practice' offers the reader tips and guidance based on the authors' vast research and instruction experience.

Multiobjective Optimization

Author: Yann Collette
Publisher: Springer Science & Business Media
ISBN: 9783662088838
Release Date: 2013-06-29
Genre: Mathematics

This text offers many multiobjective optimization methods accompanied by analytical examples, and it treats problems not only in engineering but also operations research and management. It explains how to choose the best method to solve a problem and uses three primary application examples: optimization of the numerical simulation of an industrial process; sizing of a telecommunication network; and decision-aid tools for the sorting of bids.

Principles of Linear Systems

Author: Philip E. Sarachik
Publisher: Cambridge University Press
ISBN: 0521576067
Release Date: 1997-01-28
Genre: Mathematics

Textbook on state-space methods in the analysis of linear multi-input, multi-output dynamic systems.