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An Optimization Primer : On Models, Algorithms, and Duality - Lawrence Nazareth

An Optimization Primer

On Models, Algorithms, and Duality

Paperback Published: 18th May 2004
ISBN: 9780387211558
Number Of Pages: 108

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Optimization is the art, science and mathematics of finding the "best" member of a finite or infinite set of possible choices, based on some objective measure of the merit of each choice in the set. Three key facets of the subject are:

- the construction of optimization models that capture the range of available choices within a feasible set and the measure-of-merit of any particular choice in a feasible set relative to its competitors;

- the invention and implementation of efficient algorithms for solving optimization models;

- a mathematical principle of duality that relates optimization models to one another in a fundamental way. Duality cuts across the entire field of optimization and is useful, in particular, for identifying optimality conditions, i.e., criteria that a given member of a feasible set must satisfy in order to be an optimal solution.

This booklet provides a gentle introduction to the above topics and will be of interest to college students taking an introductory course in optimization, high school students beginning their studies in mathematics and science, the general reader looking for an overall sense of the field of optimization, and specialists in optimization interested in developing new ways of teaching the subject to their students.

John Lawrence Nazareth is Professor Emeritus in the Department of Mathematics at Washington State University and Affiliate Professor in the Department of Applied Mathematics at the University of Washington. He is the author of two recent books also published by Springer-Verlag which explore the above topics in more depth, Differentiable Optimization and Equation Solving (2003) and DLP and Extensions: An Optimization Model and Decision Support System (2001).

From the reviews:

Your latest, An Optimization Primer, is a little masterpiece. Congratulations!

- George B. Dantzig, Stanford University

Your book looks very good, a particularly nice way to introduce people to the topic.

- James Renegar, Cornell University

"This book provides a very gentle introduction to three key aspects of the optimization field: models, algorithms and duality. ... The book will be of interest to college students taking an introductory course in optimization, high school students beginning their studies in Mathematics and Science, and specialists in optimization interested in developing new ways of teaching the subject to their students." (I. M. Stancu-Minasian, Zentralblatt MATH, Vol. 1103 (5), 2007)


Comments on Style and Print Size
Simple Motivating Examples
A Quintessential Optimization Problem
Duality on Bipartite Networks
A Network Flows Overview
Duality in Linear Programming
Golden Age of Optimization
An Algorithmic Revolution
Nonlinear Programming
DLP and Extensions
Optimization: The Big Picture
Bibliography
Index
About the Author
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387211558
ISBN-10: 0387211551
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 108
Published: 18th May 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 0.81
Weight (kg): 0.41

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