Computing the Newton Step: From GD to CG

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Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Explores the importance of comparing tangent vectors at different points using algorithms and finite differences.

Explores practical optimization using Manopt for manifolds, covering gradient checks, approximation errors, and Hessian computations.

Explores Taylor expansions of first order in optimization on manifolds.

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.