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Didier Henrion - Course on polynomial and LMI optimization in Prague

Date: 16/02/2015 10:00 - 23/02/2015 16:00
Place: The Czech Technical University -- Karlovo Namesti 13, 12135 Praha 2
Course on polynomial and LMI optimization in Prague, February 2015

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 
 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).