This lecture covers optimality conditions in optimization on manifolds, focusing on global and local minimum points, critical points, and the relationship between critical points and local minima on Riemannian manifolds.
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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 Riemann
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
