Optimization / Edition 2

by Kenneth Lange

Overview

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. 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 statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications.

In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.

Product Details

ISBN-13:	9781489992703
Publisher:	Springer New York
Publication date:	04/03/2015
Series:	Springer Texts in Statistics , #95
Edition description:	2nd ed. 2013
Pages:	529
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About 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.

Table of Contents

Elementary Optimization.- The Seven C’s of Analysis.- The Gauge Integral.- Differentiation.- Karush-Kuhn-Tucker Theory.- Convexity.- Block Relaxation.- The MM Algorithm.- The EM Algorithm.- Newton’s Method and Scoring.- Conjugate Gradient and Quasi-Newton.- Analysis of Convergence.- Penalty and Barrier Methods.- Convex Calculus.- Feasibility and Duality.- Convex Minimization Algorithms.- The Calculus of Variations.- Appendix: Mathematical Notes.- References.- Index.

Editorial Reviews

From the reviews:

"...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)

From the Publisher