An Introduction to Optimization on Smooth Manifolds

Optimization on Riemannian manifolds is a powerful framework that combines smooth geometry and optimization, applied in machine learning, computer vision, signal processing, and more. This text provides a mathematical grounding for using these tools, with an intuitive charts-last approach and practical examples.

Format: Paperback / softback
Length: 400 pages
Publication date: 16 March 2023
Publisher: Cambridge University Press

Optimization on Riemannian manifolds, a result of the seamless fusion of smooth geometry and optimization, has emerged as a powerful modern framework that encompasses a wide range of scientific and engineering disciplines. Machine learning, computer vision, signal processing, dynamical systems, and scientific computing are just a few of the areas where this field has made significant contributions.

In order to assist students and researchers in applied mathematics, computer science, and engineering in developing a solid mathematical foundation for confidently utilizing these tools in their research, this text introduces the concepts of differential geometry and Riemannian geometry. The text adopts a charts-last approach, which will be more intuitive from an optimizer's perspective, and all definitions and theorems are motivated by the development of time-tested optimization algorithms.

Beginning with first principles, the text proceeds to cover current research on topics such as worst-case complexity and geodesic convexity. Throughout the book, readers will find valuable tips and tricks for conducting research and implementing numerical implementations.

By integrating smooth geometry and optimization, optimization on Riemannian manifolds has opened up new avenues for solving complex problems and advancing scientific understanding. This field continues to evolve and grow, with promising applications in fields such as robotics, medical imaging, and energy optimization.

In conclusion, optimization on Riemannian manifolds is a fascinating and rapidly evolving field that has the potential to transform many aspects of science and engineering. By providing a comprehensive introduction to differential geometry and Riemannian geometry, this text aims to empower students and researchers to leverage these powerful tools in their research and drive innovation in their respective fields.

Weight: 684g
Dimension: 254 x 180 x 21 (mm)
ISBN-13: 9781009166157