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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 applied
mathematics, computer science and engineering students and
researchers gain a firm mathematical grounding to use these tools
confidently in their research. Its chart-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.
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 applied
mathematics, computer science and engineering students and
researchers gain a firm mathematical grounding to use these tools
confidently in their research. Its chart-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.
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