Manopt: Optimization on Manifolds

Related lectures (31)

Page 3 of 4

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

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

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

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Covers the concept of local frames, their construction, and limitations.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

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

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Covers the transition from Gradient Descent to Conjugate Gradients, highlighting the efficiency of CG over GD in optimization on manifolds.