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.
An invitation to optimization with Riemannian geometry for applied mathematics, computer science and engineering students and researchers.
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.
'With its inviting embedded-first progression and its many examples
and exercises, this book constitutes an excellent companion to the
literature on Riemannian optimization - from the early developments
in the late 20th century to topics that have gained prominence
since the 2008 book 'Optimization Algorithms on Matrix Manifolds',
and related software, such as Manopt/Pymanopt/Manopt.jl.' P.-A.
Absil, University of Louvain
'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
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