Information
The course will take place from Wednesday, July 22nd to Tuesday, July 28th and will be given by Maximilian Merkert. It will be held online via the web conferencing system BigBlueButton. Access details will be sent to all registered participants via e-mail.
Abstract
The topic of this compact course is optimizing a polynomial function over a feasible region defined by polynomial equations and inequalities (i.e., a semi-algebraic set). This setting allows to model a wide range of problems from various applications, but is very challenging to solve even for very restrictive special cases. The course will cover theory on polynomial optimization, which is closely linked to real algebra, as well as practical solution methods, which you can try out during hands-on exercise sessions. Topics include: Sum-of-Squares (SOS) Polynomials, Semidefinite Optimization Problems (SDPs), Positivstellensätze, Conic Duality, and Interior-Point Methods for SDPs. This is the second iteration of this compact course. The first one was taught by Gennadiy as Part 2 of a two-week course on optimization in summer 2017.
Program
The program is as follows:
| Wed, July 22 | Thu, July 23 | Fri, July 24 | Mon, July 27 | Tue, July 28 | |
|---|---|---|---|---|---|
| Introduction + sums of squares |
Stellensätze with denominators | Stellensätze without denominatrs | Conic optimization | Interior-point methods for semidefinite optimization | |
| 09:00-10:30 | Lecture | Lecture | Lecture | Lecture | Lecture |
| 10:45-12:15 | Lecture | Lecture | Lecture | Lecture | Lecture |
| 13:45-15:15 | Lecture | Lecture | Lecture | Lecture | Software session |
| 15:30-17:00 | Exercises | Exercises | Exercises | Exercises | Software session |
Registration
Please send an email to maximilian.merkert@ovgu.de if you want to participate.