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.

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.

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.

A First Course in Optimization Theory

Author: Rangarajan K. Sundaram
Publisher: Eric Treuille
ISBN: 9780521497190
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.

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.


Author: Lucien W. Neustadt
Publisher: Princeton University Press
ISBN: 9781400870530
Release Date: 2015-03-08
Genre: Technology & Engineering

This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimization problems with equality and generalized "inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a Banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, Volterra integral equations, and difference equations. Careful distinction is made throughout the analysis between "local" and "global" maximum principles. Originally published in 1977. 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.

A Theory of Constitutional Rights

Author: Robert Alexy
Publisher: Oxford University Press, USA
ISBN: 9780199584239
Release Date: 2009-12-10
Genre: Law

This classic work of constitutional theory analyzes the general structure of constitutional rights and their judicial application. It deals with a wide range of problems common to all systems of constitutional rights review - from balancing rights to deciding the limits of their scope.

Relaxation in Optimization Theory and Variational Calculus

Author: Tomas Roubicek
Publisher: Walter de Gruyter
ISBN: 9783110811919
Release Date: 1997-01-01
Genre: Mathematics

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

Classical Control Using H Infinity Methods

Author: J. William Helton
Publisher: SIAM
ISBN: 1611971365
Release Date: 1998-01-01
Genre: H [infinity symbol] control

This versatile book teaches control system design using Hînfty techniques that are simple and compatible with classical control, yet powerful enough to quickly allow the solution of physically meaningful problems. The authors begin by teaching how to formulate control system design problems as mathematical optimization problems and then discuss the theory and numerics for these optimization problems. Their approach is simple and direct, and since the book is modular, the parts on theory can be read independently of the design parts and vice versa, allowing readers to enjoy the book on many levels. The development of Hînfty engineering was one of the main accomplishments of control in the 1980s. However, until now, there has not been a publication suitable for teaching the topic at the undergraduate level. This book fills that gap by teaching control system design using Hînfty techniques at a level within reach of the typical engineering and mathematics student. It also contains a readable account of recent developments and mathematical connections. The authors treat control design problems in a physically correct way. They present a small set of specific rules that the reader can apply to convert a particular design problem to the fundamental optimization problem of Hînfty control. This precisely formulated mathematics problem can then be solved on a computer. The book introduces the control software package OPTDesign, which allows the reader to easily reproduce the calculations done in the solved examples and even try variations on them. The description of how to convert an engineering problem to a form suitable for CAD is simpler than in other books.

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.

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.

Caribbean Integration Law

Author: David S. Berry
Publisher: OUP Oxford
ISBN: 9780191649165
Release Date: 2014-02-27
Genre: Law

Caribbean Integration Law offers a comprehensive legal analysis of the current treaties and rules governing the two main regional organisations in the Caribbean, the Caribbean Community (CARICOM) and the Organisation of Eastern Caribbean States (OECS). Both organisations are operating under new treaties, the Revised Treaty of Chaguaramas and the Revised Treaty of Basseterre, respectively, which created the CARICOM Single Market and Economy, and the OECS Economic Union. The single market and economic union were built upon principles of free movement of goods, labour, and capital, and a common external tariff. This book reviews the foundations of Caribbean regional integration, the institutional frameworks of the two regional organisations, and fleshes out the scope and context of the legal systems created by the treaties. It also reviews the dispute settlement mechanisms under both treaties, including the increasingly active role of the Caribbean Court of Justice, which allows persons to enforce their treaty rights directly before the Court. The book offers selective comparisons to the current rules governing the European Union, and integrates crucial insights from the field of public international law, including the law of treaties and international institutional law.