This lecture explores the importance of comparing tangent vectors at different points, focusing on algorithms like RCG and BFGS, finite differences in R², and Lipschitz continuous gradients.
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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 transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.