Book Description

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick–slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.

The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.

In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general. ... Read more

Book Description

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references. ... Read more

Book Description

This book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. It contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results in a field to which the authors have made important contributions themselves. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.The present book can thus be used either as a textbook by graduate students or as a modern monograph by researchers in this field. ... Read more

Book Description

Most of the books in optimization are devoted to details of one or two aspect of the subject e.g. linear and nonlinear programming, stochastic programming, optimal control, stochastic dynamic programming, mixed integer programming, heuristic methods, or multi-objective programming etc., or are written for a specific discipline. The wide scope of optimization mandates extensive interaction between various disciplines in the development of the methods and algorithms, and in their fruitful application to real world problems. This book presents a discipline independent view of optimization for scientists, researchers, and analysts in various fields. It provides them opportunities to identify and apply algorithms, methods and tools from the diverse areas of optimization to their own field without getting into too much detail about the underlying theories.Audience: Researchers in various fields as well as undergraduate and graduate students in engineering, sciences, management science, and decision science. ... Read more

Reviews (1)

Still the best logic text for computer science
I've been using this book to teach introductory mathematical logic to computer science students for many years. Every year or two, I look again for something that might cover the ground better, but, despite some notational flaws and an occasional error or poor choice of phrase, this one comes out on top every time. ... Read more

Book Description

Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.

The basic idea of the LMI method in control is to approximate a given control problem via an optimization problem with linear objective and so-called LMI constraints. The LMI method leads to an efficient numerical solution and is particularly suited to problems with uncertain data and multiple (possibly conflicting) specifications.

Since the early 1990s, with the development of interior-point methods for solving LMI problems, the LMI approach has gained increased interest. One advantage of this technique is its ability to treat large classes of control problems via efficient numerical tools. This approach is widely applicable, not only in control but also in other areas where uncertainty arises. LMI techniques provide a common language for many engineering problems. Notions now popular in control, such as uncertainty and robustness, are being used in other areas through the use of LMIs. This technique is particularly attractive for industrial applications. It is well suited for the development of CAD tools that help engineers solve analysis and synthesis problems. ... Read more

Book Description

The principal objective of this book is to present a collectionof challenging test problems arising in literature studies and a widespectrum of applications. These applications include: pooling/blendingoperations, heat exchanger network synthesis, phase and chemicalreactor network synthesis, parameter estimation and datareconciliation, clusters of atoms and molecules, pump networksynthesis, trim loss minimization, homogeneous azeotropic separation,dynamic optimization and optimal control problems. Audience: This book will be of value to academic and industrialresearchers interested in algorithmic and software development ofwell-designed nonconvex optimization test problems. ... Read more

Book Description

Genetic Algorithms (GAs) have become a highly effective tool for solving hard optimization problems. As their popularity has increased, the number of GA applications has grown in more than equal measure. Genetic Algorithm theory, however, has not kept pace with the growing use and application of GAs. Most book-length treatments of GAs provide only a cursory discussion of theory and this discussion primarily focuses on the traditional view, which depends heavily on the concept of a "schema".Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory is a survey of some important theoretical contributions, many of which have been proposed and developed in the Foundations of Genetic Algorithms series of workshops. However, this theoretical work is still rather fragmented, and the authors believe that it is the right time to provide the field with a systematic presentation of the current state of theory in the form of a set of theoretical perspectives. The authors do this in the interest of providing students and researchers with a balanced foundational survey of some recent research on GAs. The scope of the book includes chapter-length discussions of Basic Principles, Schema Theory, "No Free Lunch", GAs and Markov Processes, Dynamical Systems Model, Statistical Mechanics Approximations, Predicting GA Performance, Landscapes and Test Problems.The authors have worked hard to make the book as accessible as possible for students and researchers. An undergraduate-level mathematical understanding of linear algebra and stochastic processes is assumed. For those readers who have not encountered GAs before, a comprehensive survey of GA concepts is provided and the variety of ways in which GAs can be implemented is outlined. Exercises are provided at the ends of the chapters with the express purpose of aiding understanding of the concepts discussed and to whet the reader's appetite for pursuing theoretical research in GAs. ... Read more

Book Description

The author of this book made an attempt to create the generaltheory of optimization of linear systems (both distributed and lumped)with a singular control. The book touches upon a wide range of issuessuch as solvability of boundary values problems for partialdifferential equations with generalized right-hand sides, theexistence of optimal controls, the necessary conditions of optimality,the controllability of systems, numerical methods of approximation ofgeneralized solutions of initial boundary value problems withgeneralized data, and numerical methods for approximation of optimalcontrols. In particular, the problems of optimization of linearsystems with lumped controls (pulse, point, pointwise, mobile and soon) are investigated in detail.Audience: Scientists and engineers engaged in the theory ofoptimal control of linear systems and its application in physics,ecology, economy, medicine, and other fields. Also suitable as atextbook for graduate and post-graduate students studying modernmethods in optimal control. ... Read more

Book Description

The IMA Workshop on Evolutionary Algorithms brought together many of the top researchers in the area of Evolutionary Computation for a week of intensive interaction. The field of Evolutionary Computation has developed significantly over the past 30 years and today consists of a variety of subfields such as genetic algorithms, evolution strategies, evolutionary programming, and genetic programming, each with its own algorithmic perspectives and goals. The workshop did a great deal to clarify the current state of the theory of Evolutionary Algorithms. The existing theory might be characterized as deriving from two principal approaches. There is a high level macro-theory that looks at the processing of "building blocks" and "schemata" that are shared by many good solutions when searching a problem space. There is also a low level micro-theory that builds exact Markov models of the search process. It is sometimes hard for researchers working at such different levels of abstraction to interact. The IMA workshop allowed researchers working at these different levels to present their points of view and to move toward common ground. There was real progress in communication between theorists and practitioners in the evolutionary computation field. Speakers presented applications across a wide range of problem areas. In some of those cases, theoretically motivated methods work quite well. In other cases, practitioners used domain-based methods to obtain better performance than could be achieved by using a "pure" evolutionary algorithm. Individuals on both sides went away with a better appreciation of the successes and failures of current theory. ... Read more

Reviews (1)

it deals with some of my research topics too and excellent j
The abriged version as available in India gives a brief insight on the coverage given by the author.I have done studies in the same field and would like to share my thoghts with the author who I would be obliged if his contact address be sent accross.Full review will sent to the author in due course. ... Read more

Book Description

This book provides a solid foundation and an extensive study for Mathematical Programs with Equilibrium Constraints (MPEC). It begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalization, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions.The book also describes several iterative algorithms such as a penalty based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modeling of many practical problems. ... Read more

Book Description

This volume is derived from invited talks given at a meeting celebrating Michael Powell's sixtieth birthday and focuses on innovative work in optimization and approximation theory. The individual papers, written by leading authorities in their subjects, are a mix of expository articles and surveys on new work. They have all been reviewed and edited to form a coherent volume that represents the state of the art in an important discipline within mathematics, with highly relevant applications throughout science and engineering. ... Read more

Book Description

The book provides a self-contained introduction to underlying techniques, as well as a compendium of theory and a guide to the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. Besides introductory and survey material, the book contains unique research results. The book also contains non-traditional ideas concerning non-smooth optimization. Thus, the book should be a valuable reference to applied mathematicians and computational scientists and engineers. With numerous examples and exercises, as well as leads for future research, the book can be used as a graduate text or reference on interval arithmetic, automatic differentiation and interval fixed point theory. The book can also serve as a user's guide for the nonlinear equations and optimization software, available free of charge from the author, for the author's general Fortran 90 interval arithmetic package, or for the associated automatic differentiation package.Audience: Researchers in operations research, numerical analysis, computational chemistry, computer-aided geometric design and computational geometry, robot kinematics, remote sensing. Also suitable for graduate and topics courses in numerical analysis, optimization, and operations research. ... Read more

Book Description

This new junior/senior level textbook, based on the classic Melsa-Schultz LINEAR CONTROL SYSTEMS, adds the best of modern topics such as robustness, ramifications of model inaccuracies on the design of control systems, computer examples using MATLAB, and design problems to a very successful classic textbook. It has broad applications to electrical, mechanical, chemical and aerospace engineering. ... Read more

Reviews (2)

a helpful classroom tool
clear examples, well explained, a helpful textbook

Good text for Elec., Mech., or Comp. Engineers
I read this book as part of a systems engineering introductory course.I found it to be very helpful and easy to understand.The book is well organized, and the contents of the various chapters flow together smoothly.One critique is that this book would have benefited from a greater varietyof practical examples. Instead it continually used a motor model.Whilethis example was very usefull, I would have liked to have seen some otherexamples. Overall, a solid text. ... Read more

Book Description

Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications.Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved.Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering. ... Read more

Reviews (1)

Way to go Dr. D!
This was one of the best books I've read. Even if you are just a high school principal, you are a tremendous writer and I hope you continue to strike fear into the hearts of readers everywhere! You rock Triple D! ... Read more

Reviews (1)

An excellent book
My special field is neither statistics nor math. My reading this book was for research purpose. I enjoyed reading it, though it contains a few of "printing" mistakes.

The chapter 6 is somehow hard-to-find. I believe Talagrand's isoperimetric theory has wide range of applications. But it is not easy to read his original article (which, besides, is more than 100-page long). The chapter gives a very informative introduction to the theory. ... Read more