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Perturbation Theory in Mathematical Programming and Its Applications

Author: Evgenij S. Levitin

Publisher:

Published: 1994-09-06

Total Pages: 416

ISBN-13:

Presents the author's research of local parametric optimization in the finite-dimensional case. This book provides a clear and complete formulation of the main perturbation theory problems for finite-dimensional optimization as well as new mathematical methods to analyze these problems. Using a unified approach, the author has developed a general perturbation theory for finite-dimensional extremum problems. Within the framework of this theory, methods for studying perturbed problems in zero-, first- and second-order approximations have been developed.

Analytic Perturbation Theory and Its Applications

Author: Konstantin E. Avrachenkov

Publisher: SIAM

Published: 2013-12-11

Total Pages: 384

ISBN-13: 1611973139

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Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.

Mathematical Programming with Data Perturbations

Author: Anthony V. Fiacco

Publisher: CRC Press

Published: 2020-09-23

Total Pages: 456

ISBN-13: 1000117111

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Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.

Mathematical Programming with Data Perturbations

Author: Anthony V. Fiacco

Publisher: CRC Press

Published: 1997-09-19

Total Pages: 460

ISBN-13: 9780824700591

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Perturbation Methods

Author: Ali H. Nayfeh

Publisher: John Wiley & Sons

Published: 2008-09-26

Total Pages: 437

ISBN-13: 3527617612

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The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

Perturbations

Author: James A. Murdock

Publisher: SIAM

Published: 1999-01-01

Total Pages: 358

ISBN-13: 9781611971095

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Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

Singular Perturbation Theory

Author: R.S. Johnson

Publisher: Springer Science & Business Media

Published: 2005-12-28

Total Pages: 305

ISBN-13: 0387232176

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The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.

Perturbation Methods with Applications in Science and Engineering

Author: İlkay Bakırtaş

Publisher: BoD – Books on Demand

Published: 2018-10-17

Total Pages: 170

ISBN-13: 1789842557

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The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.

Optimization

Author: Van Hien Nguyen

Publisher: Springer Science & Business Media

Published: 2000-03-06

Total Pages: 516

ISBN-13: 9783540669050

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The 9th Belgian-French-German Conference on Optimization has been held in Namur (Belgium) on September 7-11, 1998. This volume is a collection of papers presented at this Conference. Originally, this Conference was a French-German Conference but this year, in accordance with the organizers' wishes, a third country, Belgium, has joined the founding members of the Conference. Hence the name: Belgian French-German Conference on Optimization. Since the very beginning, the purpose of these Conferences has been to bring together researchers working in the area of Optimization and partic ularly to encourage young researchers to present their work. Most of the participants come from the organizing countries. However the general ten dancy is to invite outside researchers to attend the meeting. So this year, among the 101 participants at this Conference, twenty researchers came from other countries. The general theme of the Conference is everything that concerns the area of Optimization without specification of particular topics. So theoretical as pects of Optimization, in addition to applications and algorithms of Opti mization, will be developed. However, and this point was very important for the organizers, the Conference must retain its convivial character. No more than two parallel sessions are organized. This would allow useful contacts between researchers to be promoted. The editors express their sincere thanks to all those who took part in this Conference. Their invaluable discussions have made this volume possible.

Mathematical Programming with Data Perturbations II, Second Edition

Author: Fiacco

Publisher: CRC Press

Published: 2020-09-24

Total Pages: 174

ISBN-13: 1000153436

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This book presents theoretical results, including an extension of constant rank and implicit function theorems, continuity and stability bounds results for infinite dimensional problems, and the interrelationship between optimal value conditions and shadow prices for stable and unstable programs.