principles of optimization theory

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Principles Of Optimization Theory

Author : C. R. Bector
ISBN : UOM:39015060898023
Genre : Mathematics
File Size : 60. 16 MB
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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
ISBN : 9780486136950
Genre : Mathematics
File Size : 84. 11 MB
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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.


Author : Lucien W. Neustadt
ISBN : 9781400870530
Genre : Technology & Engineering
File Size : 74. 13 MB
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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.

Entropy Optimization Principles With Applications

Author : Jagat Narain Kapur
ISBN : UOM:39015022261658
Genre : Reference
File Size : 67. 89 MB
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Entropy optimization has become a powerful tool for data analysis and problem solving that has an infinite array of real-world applications. This senior-level textbook provides a unified conceptual framework for the study of probabilistic systems with its elucidation of three key concepts: Shannon's Information Theory, Jayne's Maximum Entropy Principle, and Kullback's Minimum Cross-Entropy Principle. A wide array of real-world problems and applications are included that will establish the usefulness of these methods for any discipline looking at probabilistic systems and information (such as engineering, statistics, economics, and operations research). This textbook, complete with exercises, will leave students with the ability to apply these principles to new problems. The first true textbook that provides an interdisciplinary approach to entropy optimization principles with numerous applications and exercises Applies principles to a diverse assortment of applications in statistics, thermodynamics, pattern recognition, spectral analysis, queuing theory, and parameter estimation problems Will be of use to all engineering students looking at probabilistic systems, as well as to students of statistics, operations research and economics

Foundations Of Optimization

Author : Osman Güler
ISBN : 0387684077
Genre : Business & Economics
File Size : 83. 84 MB
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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.

Algorithmic Principles Of Mathematical Programming

Author : Ulrich Faigle
ISBN : 9789401598965
Genre : Mathematics
File Size : 55. 27 MB
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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.

Optimization Theory

Author : F. Giannessi
ISBN : 9781461302957
Genre : Mathematics
File Size : 72. 64 MB
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This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to express their thanks to the authors for their contributions in this volume, and the anonymous referees for their valu able comments. Special thanks are directed to our sponsors, the Hun garian Academy of Sciences, the National Committee for Technological Development, the Hungarian National Science Foundation, and last but not least, the Hungarian Operational Research Society. We would like to thank John Martindale from Kluwer Academic Publishers for helping us produce this volume, Eva Nora Nagy for cor rections and proof-readings, and Peter Dombi for his excellent work on typesetting and editing the manuscript.

A First Course In Optimization Theory

Author : Rangarajan K. Sundaram
ISBN : 9781139643153
Genre : Business & Economics
File Size : 57. 43 MB
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This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

Practical Mathematical Optimization

Author : Jan Snyman
ISBN : 9780387243498
Genre : Mathematics
File Size : 29. 21 MB
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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.

Optimization Theory And Applications

Author : L. Cesari
ISBN : 9781461381655
Genre : Science
File Size : 47. 48 MB
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This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.

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