Ｒによる非制約的最適化入門（テキスト） Introduction to Unconstrained Optimization with R

Mishra, Shashi Kant/ Ram, Bhagwat

Springer Verlag, Singapore（2020/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 304 p.
• 言語 ENG
• 商品コード 9789811508936
• DDC分類 511

Full Description

This book discusses unconstrained optimization with R—a free, open-source computing environment, which works on several platforms, including Windows, Linux, and macOS. The book highlights methods such as the steepest descent method, Newton method, conjugate direction method, conjugate gradient methods, quasi-Newton methods, rank one correction formula, DFP method, BFGS method and their algorithms, convergence analysis, and proofs. Each method is accompanied by worked examples and R scripts. To help readers apply these methods in real-world situations, the book features a set of exercises at the end of each chapter. Primarily intended for graduate students of applied mathematics, operations research and statistics, it is also useful for students of mathematics, engineering, management, economics, and agriculture.

Contents

1. Introduction.- 2. Mathematical Foundations.- 3. Basics of R.- 4. First Order and Second Order Necessary Conditions.- 5. One Dimensional Optimization Methods.- 6. Steepest Descent Method.- 7. Newton's Method.- 8. Conjugate Direction Methods.- 9. Quasi-Newton Methods.