Optimization on Manifolds

Related lectures (32)

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Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

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

Covers the Grassmann manifold and retractions on submanifolds.

Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.

Explores truncated conjugate gradients for solving the trust-region subproblem in optimization on manifolds efficiently.

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

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