Elements of Classical and Geometric Optimization

This textbook covers both classical and geometric optimization methods,including deterministic and stochastic schemes,and is written for senior undergraduate and graduate students in applied science and engineering disciplines. It includes online resources and MATLAB codes.

Format: Hardback
Length: 484 pages
Publication date: 25 January 2024
Publisher: Taylor & Francis Ltd

This comprehensive textbook delves into both classical and geometric aspects of optimization, employing a wide range of methods, both deterministic and stochastic, within a single volume. Its accessibility to non-mathematicians makes it an ideal study material for senior undergraduate and graduate students pursuing degrees in civil, mechanical, aerospace, electrical, electronics, and communication engineering.

The book encompasses a diverse range of topics, including:

Derivative-Based Methods of Optimization: This section explores the use of derivatives to find optimal solutions to optimization problems. It covers techniques such as gradient descent, Newton's method, and quasi-Newton methods, which are widely employed in various fields.

Direct Search Methods of Optimization: Direct search methods involve iteratively searching for the optimal solution by evaluating candidate solutions at each step. These methods include hill climbing, simulated annealing, and genetic algorithms, among others.

Basics of Riemannian Differential Geometry: This section provides a foundational understanding of Riemannian differential geometry, which is essential for the development of geometric optimization methods. It covers topics such as manifolds, tangent spaces, curvature, and geodesics, which are crucial in analyzing and solving optimization problems in geometric settings.

Geometric Methods of Optimization using Riemannian Langevin Dynamics: This section introduces geometric optimization methods that utilize Riemannian Langevin dynamics. These methods combine the principles of geometric optimization with the stochastic dynamics of Langevin equations, allowing for the exploration of complex optimization problems in dynamic environments.

Stochastic Analysis on Manifolds and Geometric Optimization Methods: This section explores the application of stochastic analysis on manifolds to geometric optimization problems. It covers topics such as Markov chains, stochastic differential equations, and Monte Carlo methods, which are used to simulate and analyze optimization processes in uncertain environments.

The textbook is accompanied by comprehensive online resources, including MATLAB codes, which are uploaded on the publisher's website. These codes provide practical implementations and examples of the optimization techniques discussed in the book, making it an invaluable resource for students and practitioners alike.

Designed primarily for senior undergraduate and graduate students in all applied science and engineering disciplines, this textbook serves as a primary or supplementary text for courses on classical and geometric optimization. Its comprehensive coverage, coupled with its accessible language, makes it an essential tool for anyone seeking to advance their knowledge and expertise in this field.

Weight: 1130g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367560164