Lecture

Riemannian gradient descent

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In course

MATH-512: Optimization on manifolds

We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...

Description

This lecture covers Riemannian gradient descent, focusing on Taylor expansions, first-order optimality conditions, algorithm templates, line search, sufficient decrease, regularity conditions, and critical points. It also discusses the behavior of local minimizers and the concept of critical points. The instructor explains the pull back of functions through retractions, the definition of local minimizers, and the necessary conditions for a point to be a critical or stationary point. The lecture concludes with a theorem on the sequence produced by Riemannian gradient descent under specific assumptions.

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Instructor

Nicolas Boumal

Teaching & PhD PhD Students Andreea-Alexandra Musat Past EPFL PhD Students Christopher Criscitiello, Quentin Rebjock Courses Continuous optimization MATH-329 This course introduces students to continuous, nonlinear optimization. We study the theory of optimization with continuous variables (with full proofs), and we analyze and implement important algorithms to solve constrained and unconstrained problems. Linear Algebra MATH-111(e) The purpose of the course is to introduce

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