Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-65-15B-K-7

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

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h

Basedata

SWS 2V
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

Notice

This course will not be offered again.

Contents

  • Levi-Civita connection,
  • curvature,
  • Hessian,
  • second-order optimization methods, Newton-like methods,
  • Jacobi fields,
  • Hadamard manifolds: introduction, proximal point methods, optimization methods from convex analysis,

• (possible outlooks: Lie groups and Lie algebras, integration on manifolds).

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.

References to Course [MAT-65-15B-K-7]

Module Name Context
[MAT-65-15-M-7] Optimization on Manifolds P: Obligatory 2V, 4.5 LP, AUSL