Course MAT-65-15A-K-7
Optimization on Manifolds - Part 1 (2V+1U, 4.5 LP, AUSL)
Course Type
SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
---|---|---|---|---|---|
- | K | Lecture with exercise classes (V/U) | 4.5 CP | 93 h | |
2 | V | Lecture | 28 h | ||
1 | U | Exercise class (in small groups) | 14 h | ||
(2V+1U) | 4.5 CP | 42 h | 93 h |
Basedata
SWS | 2V+1U |
---|---|
CP, Effort | 4.5 CP = 135 h |
Position of the semester | 1 Sem. irreg. |
Level | [7] Master (Advanced) |
Language | [EN] English |
Lecturers | |
Area of study | [MAT-SPAS] Analysis and Stochastics |
Livecycle-State | [AUSL] Phase-out period |
Contents
- Gateaux and Fréchet differentiability,
- differentiable finite-dimensional manifolds: charts, atlas, tangent vectors and tangent spaces, vector fields, differential of a mapping,
- Riemannian metric, geodesics, Christoffel symbols, exponential map and logarithmic map,
- Hopf-Rinow theorem,
- first-order optimization, descent methods,
- examples of manifolds: spheres, hyperbolic spaces, positive definite matrices, probability simplex, Grassmann manifolds, Stiefel manifolds, special Euclidean group, rotation group,
- linear connection and parallel transport.
Literature
- P.-A. Absil, R. Mahony, R. Sepulchre: Optimization Algorithms on Matrix Manifolds,
- J. Jost: Riemannian Geometry and Geometric Analysis,
- J. M. Lee: Introduction to Smooth Manifolds,
- S. Helgason: Differential Geometry, Lie Groups and Symmetric Spaces,
- D. Gromoll, W. Klingenberg, and W. Meyer: Riemannsche Geometrie im Großen.
Materials
Further literature will be announced in the lecture.
Requirements for attendance (informal)
Modules:
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)
Courses
- [MAT-12-23-K-3] Introduction to Functional Analysis (2V+1U, 4.5 LP)
- [MAT-12-27-K-3] Vector Analysis (2V+1U, 4.5 LP)
Requirements for attendance (formal)
None
References to Course [MAT-65-15A-K-7]
Module | Name | Context | |
---|---|---|---|
[MAT-65-15A-M-7] | Optimization on Manifolds - Part 1 | P: Obligatory | 2V+1U, 4.5 LP, AUSL |
[MAT-65-15-M-7] | Optimization on Manifolds | P: Obligatory | 2V+1U, 4.5 LP, AUSL |
Notice