EECI GSC course on LMIs for optimization and control
(Didier Henrion, LAAS-CNRS, Toulouse, France and FEL-CVUT, Prague, Czech Republic)

Online course organized by the Department of Information Engineering, Computer Science and Mathematics of the University of L'Aquila, Italy from 26 to 30 April 2021

Venue and dates

The course is given online. It consists of 14 lectures of 90 minutes each, given on Monday 26 (2pm-5:30pm), Tuesday 27 (9:30am-1pm and 2pm-5:30pm), Wednesday 28 (2pm-5:30pm), Thursday 29 (9:30am-1pm and 2pm-5:30pm) and Friday 30 April (9:30am-1pm) 2021, following this schedule.


The course outline and keywords are described in this document. Video recordings of the lectures are available below:

  • Lecture 1 - Introduction to the course and the participants
  • Lecture 2 (sound only) - Background on convexity and cones
  • Lecture 3 (sound only) - Geometry of the semidefinite cone
  • Lecture 4 - Finite-dimensional conic duality
  • Lecture 5 - Semidefinite programming duality
  • Lecture 6 - Matlab demo with SeDuMi, MOSEK and YALMIP - scripts
  • Lecture 7 - Background on measure theory, infinite-dimensional conic duality
  • Lecture 8 - Positive polynomials and moments, the moment-SOS hierarchy
  • Lecture 9 - Solutions to exercises and the moment-SOS hierarchy
  • Lecture 10 - Polynomial optimization - slides with exercises and notes
  • Lecture 11 - Polynomial optimization continued - Matlab demo with GloptiPoly - scripts
  • Lecture 12 - Positively invariant sets - slides with exercises and notes
  • Lecture 13 - Polynomial optimal control - slides with exercises and notes
  • Lecture 14 - Polynomial optimal control continued - Matlab demo with GloptiPoly - scripts

    The course follows the lecture notes:

  • D. Henrion. Optimization on linear matrix inequalities for polynomial systems control. International Summer School of Automatic Control, Grenoble, France, September 2014.

    Homeworks and exam

    Homeworks are given during the course. A written examination is available on request. Certificates of attendance can be provided on request.

    Last updated on 30 April 2021.