Basics of Optimization Theory

2023
ISBN: 978-3-031-29218-7
Verlag: Springer

Buch, Englisch, 143 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 443 g

Reihe: Synthesis Lectures on Mathematics & Statistics

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

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Snider, Arthur David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

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

Über Autor(innen)

Arthur David Snider, PhD., is a Professor Emeritus in the Departments of Mathematics, Physics, and Electrical Engineering at the University of South Florida. He has 50+ years of experience in modeling physical systems in the areas of heat transfer, electromagnetics, microwave circuits, and orbital mechanics, as well as the mathematical areas of numerical analysis, signal processing, differential equations, and optimization.