Convex Optimization

This course took place several times between 2016 and 2020 at FU Berlin, TU Berlin and Uni Kassel and is based on the book Convex Optimization, by S. Boyd and L. Vandenberghe (2004).

It proposes a comprehensive introduction to the theory of Convex Optimization, showing how a variety of situations can be modelled using this paradigm, and reviews the different algorithmic methods to solve these problems.

List of addressed topics:

• Convex Geometry
• Conic Programming
• Convex Programming and Duality
• Applications in Combinatorial Optimization & Data science
• Ellipsoid Method, Interior Point Methods and First-order Methods.

Handout:

In addition to the book “Convex Optimization” of Boyd & Vandenberghe, this course is based on further references which are cited in the respective chapters.

• Chapter 1: Introduction & Preliminaries
• Chapter 2: Convex Geometry
• Chapter 3: Convex Functions
• Chapter 4: Convex Optimization
• Chapter 5: The Ellipsoid Method
• Chapter 6: Conic Programming
• Chapter 7: Duality
• Chapter 8: Applications in Combinatorial Optimization
• Chapter 9: The Lasserre Hierarchy
• Chapter 10: Interior Point Methods
• Chapter 11: Applications to Data Science
• Chapter 12: First-Order Methods
• Chapter 13: Robust Optimization