University Center for Mathematical Modeling, Applied Analysis and Computational Mathematics is organizing the regular semester seminar. The seminar will take place on 15th December 2014 in lecture room K2 from 8:30 to 12:10. Seminar schedule is attached. You are all cordially invited to attend the seminar.

Contributed by: Didier Henrion, henrion@laas.fr.

Course on polynomial and LMI optimization with applications in control by Didier Henrion, LAAS-CNRS, Toulouse, France and Czech Technical University in Prague, Czech Republic

http://homepages.laas.fr/henrion/courses/lmi15

Venue and dates

The course is given at the Charles Square campus of the Czech Technical University, in the historical center of Prague (Karlovo Namesti 13, 12135 Praha 2). It consists of six two-hour lectures, given on Monday 16, Thursday 19 and Monday 23 February, 2015, from 10am to noon and from 2pm to 4pm.

Registration

There is no admission fee, students and reseachers from external institutions are particularly welcome, but please send an e-mail to henrion@laas.fr to register.

Target audience

This is a course for graduate students or researchers with some background in linear algebra, convex optimization and linear control systems.

Outline

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate approximate solutions in floating point arithmetic.

In the first part of the course we describe semidefinite programming (SDP) as an extension of linear programming (LP) to the cone of positive semidefinite matrices. We investigate the geometry of spectrahedra, convex sets defined by linear matrix inequalities (LMIs) or affine sections of the SDP cone. We also introduce spectrahedral shadows, or lifted LMIs, obtained by projecting affine sections of the SDP cones. Then we review existing numerical algorithms for solving SDP problems.

In the second part of the course we describe several recent applications of SDP. First, we explain how to solve polynomial optimization problems, where a real multivariate polynomial must be optimized over a (possibly nonconvex) basic semialgebraic set. Second, we extend these techniques to ordinary differential equations (ODEs) with polynomial dynamics, and the problem of trajectory optimization (analysis of stability or performance of solutions of ODEs). Third, we conclude this part with applications to optimal control (design of a trajectory optimal w.r.t. a given functional).

Miroslav Bulíček has been awarded by the Czech mathematical society award. Congratulations!

Substantial part of our group is involved in ERC-CZ project Implicitly constituted material models: from theory through model reduction to efficient numerical methods. During the last week we were organizing conference “Modeling, analysis and computing in nonlinear partial differential equations”. With the help of Vojtěch Ciml and his platform SlidesLive, we have recorded all the lectures, and we have made them publicly available on the Internet. If you want to see the lectures, please have a look. (Just now you can probably see only a fraction of the lectures, the rest of the lectures will be uploaded soon.)

Dear students,

winter semester 2014/2015 is ready to begin. The meeting of all students of mathematical modelling (fixing the schedule for optional lectures, brief discussion on topics of bachelor/master thesis) will take place on Thursday, October 2 at 13:20 in lecture room K358MUUK (seminar room of the Mathematical Instititute, Sokolovská 83, third floor). We ask especially first year students to attend the meeting.

During the first thirty minutes we will be talking mainly to the first year students, the discussion concerning the the optional lectures and seminars is expected to start at 13:50.

A preliminary schedule for the winter semester 2014/2015 is available in SIS.

Czech Network for Mathematics in Industry, on whose foundation we have significantly contributed, has become a member of the European Service Network of Mathematics for Industry and Innovation. European Service Network of Mathematics for Industry is a new initiative to boost mathematics for industry in Europe.

Faculty of Mathematics and Physics invites you to the Thirteenth Jarník lecture Ill-Posed Problems in Probability which will be delivered by prof. RNDr. Lev Klebanov, DrSc. (Department of Probability and Mathematical Statistics). The lecture will take place on Wednesday, October 1st, 2014 at 14:00 pm. in V. Jarník lecture hall (M1), 2nd floor, Ke Karlovu 3, Praha 2.

Winter semester 2014/2015 is ready to begin:

• A preliminary schedule for the winter semester 2014/2015 is available in SIS.
• The meeting of all students of mathematical modelling (fixing the schedule for optional lectures, brief discussion on topics of bachelor/master thesis topics) will take place on Thursday, October 2. This is a preliminary date, please follow the website for updates!

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English translation of the list of topics for oral part of the state exam (MSc. study, study programme Mathematical Modelling in Physics and Technology) is available on the study web page. Czech version of the list has been posted earlier this year, see the Czech version of the study web page.

If you find some misprints, please report them to Vít Průša (prusv@kalin.mff.cuni.cz).