Seminar Mathematics and Computation: Convex Optimization (Summer 2025)

Type: Seminar
Programs: MSc CS, Math
Organizers: Vladimir Lysikov, Michael Walter
Time and Place:
First meeting:
Credits: 3-5 CP
Contact time: 2 SWS
Language: English
Course number: 211136
Links: Registration

This is a seminar series whose theme changes every term. It should be of particular interest to Master’s students of computer science and mathematics. We particularly recommend it as preparation for a thesis project.

This term, the topic will be Convex Optimization.

Themes of past semesters:

How can I join?

To apply for this seminar, please see the Moodle course of the faculty.

Required prior knowledge

The seminar requires a strong interest and background in theoretical computer science and mathematics.

Description

Many problems can be phrased as optimization problems, and hence optimization algorithms are employed widely in theory and practice, in all areas of science, technology, and economics. This seminar focuses on the theory of convex optimization, which is concerned with a class of particularly well-behaved optimization problems for which an exact solution can be found efficiently (a seminal result in theoretical computer science). We will discuss basic properties of convex functions, important algorithms and their convergence, and various applications of convex optimization, including some examples where the convexity of the problem is not obvious from its immediate description.

Possible topics

  1. Basic notions of convexity: convex combinations, convex sets, convex and concave functions, uniqueness of extremal values

  2. Gradient descent methods for unconstrained optimization and its iteration complexity

  3. Projected gradient descent for constrained convex optimization

  4. Oracles for convex constraints, ellipsoid method

  5. Accelerated gradient descent

  6. Second-order (Newton) method, local convergence

  7. Convex cones, conic programming, duality for conic programming

  8. Matrix scaling, Sinkhorn’s algorithm

  9. Semidefinite programming

  10. Sum of Squares (SOS) hierarchy for polynomial optimization

References

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