Optimization / Edition 1

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Overview

This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students' skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on convexity serves as bridge between linear and nonlinear programming and makes it possible to give a modern exposition of linear programming based on the interior point method rather than the simplex method. The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes graduate students in applied mathematics, computational biology, computer science, economics, and physics as well as upper division undergraduate majors in mathematics who want to see rigorous mathematics combined with real applications.
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Editorial Reviews

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"...An excellent, imaginative, and authoritative text on the difficult topic of modeling the problems of multivariate outcomes with different scaling levels, different units of analysis, and different study designs simultaneously." Biometrics, March 2005

"...As a textbook, Optimization does provide a valuable introduction to an important branch of applicable mathematics." Technometrics, August 2005

"...I found Optimization to be an extremely engaging textbook....the text is ideal for graduate students or researchers beginning research on optimization problems in statistics. There is little doubt that someone who worked through the text as part of a reading course or specialized graduate seminar would benefit greatly from the author's perspective..." Journal of the American Statistical Association, December 2005

"This is a book on optimization theory that includes some of the background mathematics necessary to understand … . provides a good overview of graduate-level topics in optimization, including some of the supporting mathematics and some applications. … The book has some every nice exercise sets to illuminate and extend the material covered in the textbook, as well as an extensive bibliography. … a valuable introduction to an important branch of applicable mathematics." (Marvin H.J. Gruber, Technometrics, Vol. 47 (3), August, 2005)

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Product Details

  • ISBN-13: 9780387203324
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 6/17/2004
  • Series: Springer Texts in Statistics Series
  • Edition description: 2004
  • Edition number: 1
  • Pages: 268
  • Product dimensions: 0.75 (w) x 6.14 (h) x 9.21 (d)

Meet the Author

Kenneth Lange is the Rosenfeld Professor of Computational Genetics at UCLA. He is also Chair of the Department of Human Genetics and Professor of Biomathematics and Statistics. At various times during his career, he has held appointments at the University of New Hampshire, MIT, Harvard, the University of Michigan, the University of Helsinki, and Stanford. He is a fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Institute for Medical and Biomedical Engineering. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied shastic processes. Springer previously published his books Mathematical and Statistical Methods for Genetic Analysis, Numerical Analysis for Statisticians, and Applied Probability, all in second editions.

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Table of Contents

1 Elementary optimization 1
2 The seven C's of analysis 19
3 Differentiation 43
4 Karush-Kuhn-Tucker theory 69
5 Convexity 93
6 The MM algorithm 119
7 The EM algorithm 137
8 Newton's method 155
9 Conjugate gradient and quasi-Newton 175
10 Analysis of convergence 191
11 Convex programming 207
App The normal distribution 233
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