Basics of Optimization Theory (Synthesis Lectures on Mathematics & Statistics)

Snider, Arthur David

Springer International Publishing AG（2023/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 143 p.
• 商品コード 9783031292187

Full Description

This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate gradients, and the Karush-Kuhn-Tucker-John conditions. Each topic is developed in terms of a specific physical model, so that the strategy behind every step is motivated by a logical, concrete, easily visualized objective. A quick perusal of the Fibonacci search algorithm provides a simple and tantalizing first encounter with optimization theory, and a review of the max-min exposition of one-dimensional calculus prepares readers for the more sophisticated topics found later in the book. Notable features are the innovative perspectives on the simplex algorithm and Karush-Kuhn-Tucker-John conditions as well as a wealth of helpful diagrams. The author provides pointers to references for readers who would like to learn more about rigorous definitions, proofs, elegant reformulations and extensions, and case studies. However, the book is sufficiently self-contained to serve as a reliable resource for readers who wish to exploit commercially available optimization software without investing the time to develop expertise in its aspects.
This book also:

Features innovative perspectives on the simplex algorithm and Krushal-Kuhn-Tucker-John conditions
Serves as a resource for readers to use the tools of optimization without needing to acquire expertise in the theory
Features  plentiful resources that focus on rigorous definitions, proofs, and case studies

Contents

A Preliminary Note.- Fibonnacci Search.- Linear Programming.- Nonlinear Programming in One Dimension.- Nonlinear Multidimensional Optimization.- Constrained Optimization.