Course MAT-65-15A-K-7

Optimization on Manifolds - Part 1 (2V+1U, 4.5 LP, AUSL)

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

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	Steidl, Gabriele, Prof. Dr. (PROF \| DEPT: MAT)
Area of study	[MAT-SPAS] Analysis and Stochastics
Livecycle-State	[AUSL] Phase-out period

This course was offered for the last time in SS 2018.

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.

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.

Further literature will be announced in the lecture.

None

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