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 and can serve as a bridge to more advanced treatises on nonlinear and convex programming. 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.

Klappentext

Lange is a Springer author of other successful books.

This is the first book that emphasizes the applications of optimization to statistics.

The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics.

Inhalt

1 Elementary Optimization.- 2 The Seven C's of Analysis.- 3 Differentiation.- 4 Karush-Kuhn-Tucker Theory.- 5 Convexity.- 6 The MM Algorithm.- 7 The EM Algorithm.- 8 Newton's Method.- 9 Conjugate Gradient and Quasi-Newton.- 10 Analysis of Convergence.- 11 Convex Programming.- Appendix: The Normal Distribution.- A.1 Univariate Normal Random Variables.- A.2 Multivariate Normal Random Vectors.- References.