An Introduction to Optimization on Smooth Manifolds - Hardcover

Boumal, Nicolas

Hardcover

ISBN 10: 1009166174 ISBN 13: 9781009166171

Publisher: Cambridge University Press, 2023

Synopsis

Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.

About this title

About the Author

Nicolas Boumal is Assistant Professor of Mathematics at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland, and an Associate Editor of the journal Mathematical Programming. His current research focuses on optimization, statistical estimation and numerical analysis. Over the course of his career, Boumal has contributed to several modern theoretical advances in Riemannian optimization. He is a lead-developer of the award-winning toolbox Manopt, which facilitates experimentation with optimization on manifolds.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2023
• Language: English
• ISBN 10: 1009166174
• ISBN 13: 9781009166171
• Binding: Hardcover
• Number of pages: 400