An Introduction to Optimization on Smooth Manifolds

Erscheinungsjahr 2023
ISBN: 978-1-009-16615-7
Verlag: Cambridge University Press

Buch, Englisch, 400 Seiten, Format (B × H): 180 mm x 252 mm, Gewicht: 685 g

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.

Autoren/Hrsg.

Boumal, Nicolas

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Mustererkennung, Biometrik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Notation; 1. Introduction; 2. Simple examples; 3. Embedded geometry: first order; 4. First-order optimization algorithms; 5. Embedded geometry: second order; 6. Second-order optimization algorithms; 7. Embedded submanifolds: examples; 8. General manifolds; 9. Quotient manifolds; 10. Additional tools; 11. Geodesic convexity; References; Index.

Über Autor(innen)

Boumal, Nicolas
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.