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Module Guide since WS 2023/24

Modul MA5035-KP05

Non-smooth Optimization and Analysis (NiOpAnKP05)

Duration:


1 Semester
Turnus of offer:


irregularly
Credit points:


5
Course of studies, specific field and terms:
  • Master CLS 2023 (optional subject), mathematics, 2nd or 4th semester
  • Bachelor CLS 2023 (optional subject), mathematics, 6th semester
  • Master CLS 2016 (optional subject), mathematics, 2nd or 4th semester
  • Bachelor CLS 2016 (optional subject), mathematics, 6th semester
Classes and lectures:
  • Non-smooth Optimization and Analysis (exercise, 1 SWS)
  • Non-smooth Optimization and Analysis (lecture, 2 SWS)
Workload:
  • 30 Hours work on project
  • 65 Hours private studies and exercises
  • 45 Hours in-classroom work
  • 10 Hours exam preparation
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:
Responsible for this module:
Teachers:
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:

Prerequisites for attending the module:
- None (Familiarity with the topics of the required modules is assumed, but the modules are not a formal prerequisite for attending the course).

Prerequisites for the exam:
- Homework assignments and their presentation are ungraded examination prerequisites which have to be completed and positively evaluated before the first examination.

Examination:
- MA5035-L1: Non-smooth Optimization and Analysis, written examination (90min) or oral examination (30 min) as decided by examiner, 100 % of final mark

Letzte Änderung:
22.2.2022