Synopses & Reviews
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available.Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field.Above all, the authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.MMOR Mathematical Methods of Operations Research, 2001: "The book looks very suitable to be used in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas.... I recommend this excellent book to everyone who is interested in optimization problems."
Review
"The main goal of the book is to give a comprehensive description of the most powerful, state-of-the-art techniques for solving optimization problems The book is addressed in general to the people interested in solving optimization problems, and may be used as a (two-semester) graduated-level course in optimization for the engineering, operations research, computer science, and mathematics departments. The presentation style of the book facilitates the self-study and direct application of practitioners in engineering, basic science, and industry. A typical chapter begins with a non-rigorous discussion of the topic at hand, including figures and diagrams and excluding technical details as far as possible. The algorithms are motivated, analyzed and stated explicitly. The major theoretical results are enclosed and, in many cases, proved in a rigorous fashion. These proofs may be skipped. The examples throughout the book show how practical problems are formulated as optimization problems, and the proposed treatment of the optimization process modeling is light, serving mainly to set the stage for the algorithmic developments. ZENTRALBLATT MATH"
Synopsis
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Description
Includes bibliographical references (p. [611]-623) and index.
Table of Contents
Preface
x 1 Introduction
x 2 Fundamentals of Unconstrained Optimization
x 3 Line Search Methods
x 4 Trust-Region Methods
x 5 Conjugate Gradient Methods
x Practical Newton Methods
x 7 Calculating Derivatives
x 8 Quasi-Newton Methods
x 9 Large Scale Quasi-Newton and Partially Separable Optimization
x 10 Nonlinear Least-Square Problems
x 11 Nonlinear Equations
x 12 Theory of Constrained Optimization
x 13 Linear Programming: The Simplex Method
x 14 Linear Programming: Interior-Point Methods
x 15 Fundamentals of Algorithms for Nonlinear Constrained Optimization
x 16 Quadratic Programming
x 17 Penalty, Barrier, and Augmented Lagrangian Algorithms
x 18 Sequential Quadratic Programming
x Appendix: Background Material
x Bibliography
x Index