Elements of Classical and Geometric Optimization

Debasish Roy, G Visweswara Rao

• Publisher: CRC Press
• Year: 2024
• Print ISBN: 9780367560164
• eBook ISBN: 9781000914450
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

This comprehensive textbook covers both classical and geometric aspects of optimization using methods, deterministic and stochastic, in a single volume and in a language accessible to non-mathematicians. It will help serve as an ideal study material for senior undergraduate and graduate students in the fields of civil, mechanical, aerospace, electrical, electronics, and communication engineering.

The book includes:

• Derivative-based Methods of Optimization.
• Direct Search Methods of Optimization.
• Basics of Riemannian Differential Geometry.
• Geometric Methods of Optimization using Riemannian Langevin Dynamics.
• Stochastic Analysis on Manifolds and Geometric Optimization Methods.

This textbook comprehensively treats both classical and geometric optimization methods, including deterministic and stochastic (Monte Carlo) schemes. It offers an extensive coverage of important topics including derivative-based methods, penalty function methods, method of gradient projection, evolutionary methods, geometric search using Riemannian Langevin dynamics and stochastic dynamics on manifolds. The textbook is accompanied by online resources including MATLAB codes which are uploaded on our website. The textbook is primarily written for senior undergraduate and graduate students in all applied science and engineering disciplines and can be used as a main or supplementary text for courses on classical and geometric optimization.

Table of contents

• Cover
• Half-Title Page
• Title Page
• Copyright Page
• Table of Contents
• List of Figures
• List of Tables
• List of Acronyms
• General Notations
• Preface
• 1 Optimization Methods: A Preview
• 2 Classical Derivative-based Optimization Techniques
• 3 Classical Derivative-free Methods of Optimization
• 4 Elements of Riemannian Differential Geometry and Geometric Methods of Optimization
• 5 Stochastic Analysis on a Manifold and More on Geometric Methods
• Appendix 1 
• Appendix 2 
• Appendix 3 
• Appendix 4 
• Appendix 5 
• Index