最適化（テキスト） Optimization (Springer Texts in Statistics)

Lange, Kenneth

Springer（2004発売）

• 製本 Hardcover:ハードカバー版／ページ数 252 p.
• 商品コード 9780387203324

基本説明

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 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.
Contents: Elementary Optimization.- The Seven C's of Analysis.- Differentiation.- Karush-Kuhn-Tucker Theory.- Convexity.- The MM Algorithm.- The EM Algorithm.- Newton's Method.- Conjugate Gradient and Quasi-Newton.- Analysis of Convergence.- Convex Programming.

Full Description

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.

Contents

Elementary Optimization.- The Seven C's of Analysis.- Differentiation.- Karush-Kuhn-Tucker Theory.- Convexity.- The MM Algorithm.- The EM Algorithm.- Newton's Method.- Conjugate Gradient and Quasi-Newton.- Analysis of Convergence.- Convex Programming.