Module MA5035-KP05

Duration

1 Semester

Turnus of offer

each winter semester

Credit points

5

Course of studies, specific fields and terms:

• Master CLS 2023, optional subject, mathematics
• Bachelor CLS 2023, optional subject, mathematics
• Master CLS 2016, optional subject, mathematics
• Bachelor CLS 2016, optional subject, mathematics

Classes and lectures:

• Non-smooth Optimization and Analysis (exercise, 1 SWS)
• Non-smooth Optimization and Analysis (lecture, 2 SWS)

Workload:

• 10 hours exam preparation
• 45 hours in-classroom work
• 65 hours private studies and exercises
• 30 hours work on project

Contents of teaching:

• Introduction to non-smooth analysis: convexity, subdifferentials, existence, Legendre- Fenchel conjugate, duality
• First- and higher-order numerical optimization methods: PDHG and interior-point methods
• Approximation of discrete and non-convex problems
• Generalized derivatives and Clarke subdifferential, semismooth Newton methods
• Applications in image processing and computer vision

Qualification-goals/Competencies:

• The students understand the strengths of non-smooth models.
• They can devise and analyse models for simple problems.
• They understand the advantages, disadvantages, and application areas of each optimization method.
• They know how to select and specialize a suitable optimization method for a given model.
• Interdisciplinary qualifications:
• Students have advanced skills in modeling.
• They can translate theoretical concepts into practical solutions.
• They are experienced in implementation.
• They can think abstractly about practical problems.

Grading through:

• Written or oral exam as announced by the examiner

Requires:

• Optimization (Advanced Mathematics) (MA4031-KP08)
• Optimization (MA4030-KP08, MA4030)

Responsible for this module:

• Prof. Dr. rer. nat. Jan Lellmann

Teacher:

• Institute of Mathematics and Image Computing
• Prof. Dr. rer. nat. Jan Lellmann
• Prof. Dr. rer. nat. Jan Modersitzki

Literature:

• Rockafellar, Wets : Variational Analysis Springer
• Boyd, Vandenberghe : Convex Optimization Cambridge University Press
• Ben-Tal, Nemirovski : Lectures on Modern Convex Optimization SIAM
• Paragios, Chen, Faugeras : Handbook of Mathematical Models in Computer Vision Springer

Language:

• German and English skills required

Notes:

Last Updated:

28.11.2024