Manopt: Optimization Toolbox for Manifolds

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Related lectures (31)

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Optimization on Manifolds: Context and Applications

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Riemannian metrics and gradients: Examples and Riemannian submanifolds

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

From embedded to general manifolds: Why?

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

Riemannian metrics and gradients: Why and definition of Riemannian manifolds

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

Shells I: Mechanics of Slender Structures

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

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Orthogonal Matrices, Equivalences

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

Grassmann manifold and Retractions

Covers the Grassmann manifold and retractions on submanifolds.

Tangent vectors without embedding space: Revisiting the embedded case

Explores defining tangent vectors without an embedding space, focusing on creating tangent spaces at every point of a manifold through equivalence classes of curves.