Compact Course: Polynomial Optimization

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.


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.


The program is as follows:

Wed, July 22 Thu, July 23 Fri, July 24 Mon, July 27 Tue, July 28
+ 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

Please send an email to if you want to participate.

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