Convex Optimization

• Lecturer: Prof. Stefania Petra
• Exercises: Stefania Petra, Matthias Zisler
• Format:
  • In-person lecture were we also explain each subtopic from a top-down viewpoint.
  • Detailed lecture notes that you read on your own.
  • Exercise sheets you work on your own. Solutions will be discussed in person.
  • We will use Teams for exchanging lecture material.

• Language: English
• SWS: 4
• ECTS: 6 + 2
• Lecture Id: MM35, Spezialisierungsmodul Numerik und Optimierung
• Supplementary Practical: For participating in the optional Programming Project in the semester break you get two extra credits.
• Registration: Please register in Teams.
• Prior Knowledge: Required: Lineare Algebra and Analysis

The lecture gives an introduction into the field of convex optimization and details the most important numerical methods for the solution of convex optimization problems.

• Preliminaries: Convex sets, convex functions, convex optimization problems (LPs, QPs, SOCPs, SDPs)
• Theory: Separation theorems, duality, subdifferential calculus, existence and optimality
• Algorithms: Gradient-based methods for smooth optimization, proximal-point and splitting methods
• Applications: Convex models in mathematical imaging