Hands on with Manopt: Optimization on Manifolds

Related lectures (33)

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

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

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

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

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

Covers the Grassmann manifold and retractions on submanifolds.

Explores the definition of connections for smooth vector fields on manifolds.

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Discusses gradients on Riemannian submanifolds and the construction of local frames.

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

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Explores surfaces and curvature in 3D modeling, covering zero curvature, variable curvature, and constant canonical curvatures.

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