This minicourse will focus on theoretical and computational techniques for optimization problems with algebraic structure (in particular, those involving polynomial equations and inequalities), emphasizing the connections with techniques based on semidefinite programming (SDP). The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. We will use examples from several applied math and engineering areas, including systems and control, geometric theorem proving, and classical and quantum information theory. Among the topics covered we will have: semidefinite relaxations, sum of squares representations, hyperbolic polynomials, SDP representability of convex sets, complex and real Nullstellensatz, convex algebraic geometry, sparsity and rank minimization problems, etc.
The morning program will start at 10h00 and the afternoon program might go up to 17h00.
From 9h30: Coffee/tea.
10h00 - 12h30: Lectures (including a coffee/tea break).
12h30 - 14h30: Lunch break.
14h30 - 17h00: Lectures/Exercises/Computer demos.
For the computer demos, please bring your laptop (with Matlab).
- Lecture Notes: Algebraic Optimization and Semidefinite Optimization. File.
- A small example of an LP/SDP with YALMIP/Sedumi. File.
Get together dinner
A dinner will be organized on Thursday evening for all participants of the mini-course. Details about the restaurant will be posted later.
If you stay at the Eden Lancaster hotel, here is a
showing the route from the hotel to CWI.
You can come walking (about 45-50 minutes walking distance); it is a bit shorter if at the end you enter the area at the car entrance located on the Carolina MacGillavrylaan (see the circle mark on the google map.)
You can also come with tram 9. Tram 9 rides along Plantage Middenlaan (there is a stop close by the hotel), then along Linnaeusstraat, and then along Middenweg. Get off at the stop Kruislaan (along Middenweg at the crossing with Kruislaan) and walk along Kruislaan toward Science Park (about 15-20 minutes walking distance).
Information about tickets for tram and bus in Amsterdam
can be found at the
You can buy tickets on the tram. Note that from June 3 the OV-chipkaart
will be the only allowed ticket on buses and trams in Amsterdam. (Read more
Access to CWI: When you arrive at CWI, you can get an access card to the building at the reception, as well as a card giving you access to the wireless internet CWI network.
Lecture room: L016 (ground floor of the new wing).
Deadline for applications: May 6, 2010.
For questions related to the hotel reservation please contact Susanne van Dam (susanne at cwi.nl).
For questions about the mini-course you may contact Monique Laurent (monique at cwi.nl).