An Introduction to Optimization on Smooth Manifolds

ISBN-13: 9781009166157 / Angielski / Miękka / 2023 / 400 str.

Nicolas (Ecole Polytechnique Federale de Lausanne) Boumal

Opis

An invitation to optimization with Riemannian geometry for applied mathematics, computer science and engineering students and researchers.

Recenzje

'This new book by Nicolas Boumal focuses on optimization on manifolds, which appears naturally in many areas of data science. It successfully covers all important and required concepts in differential geometry with an intuitive and pedagogical approach which is adapted to readers with no prior exposure. Algorithms and analysis are then presented with the perfect mix of significance and mathematical depth. This is a must-read for all graduate students and researchers in data science.' Francis Bach, INRIA

Spis treści

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.