French National Research Agency (ANR) project
GEOLMI - Geometry and Algebra of Linear Matrix Inequalities with Systems Control Applications

Research topics

  • Geometry of determinantal varieties
  • Positive polynomials
  • Computational algebraic geometry
  • Semidefinite programming
  • Systems control applications

    Research areas

  • Pure mathematics (real and complex algebraic geometry)
  • Applied mathematics (computational algebraic geometry, optimization, mathematical programming)
  • Engineering sciences (systems control)

    Period

    2011 - 2015

    Participants

  • Grenoble: Roland Hildebrand, Jérôme Malick, LJK-CNRS, Univ. Joseph Fourier de Grenoble
  • Nice: Laurent Busé, Bernard Mourrain, Evelyne Hubert, INRIA Sophia Antipolis Méditerranée
  • Paris: Jean-Charles Faugère, Mohab Safey El Din, Philippe Trébuchet, LIP6-CNRS Univ. Pierre et Marie Curie, INRIA Paris Rocquencourt
  • Pau: Daniele Faenzi, Jean Vallès, LMA-CNRS, Univ. de Pau et des Pays de l'Adour
  • Rennes: Michel Coste, Ronan Quarez, Marie-Françoise Roy, IRMAR-CNRS, Univ. de Rennes
  • Toulouse: Didier Henrion, Jean-Bernard Lasserre, LAAS-CNRS, Univ. de Toulouse

    Research associates

    The project funds several PhD theses and post-doctoral fellowships. Interested candidates please contact us.

  • PhD thesis: Algorithms of real algebraic geometry for systems control and aerospace applications, co-supervised by Mohab Safey El Din (Paris) and Didier Henrion (Toulouse).

    Context

    The project is an outgrowth of a previous PEPS (mutildisciplinary exploratory project) funded by CNRS from January 2008 to December 2009 and which culminated with an international workshop.

    Events

  • Spring 2011: the Toulouse group is awarded a grant from the Foundation Simone and Cino Del Duca of the Institut de France, upon recommendation by a committee of the French Academy of Sciences, see this article (in French).

  • Fall 2011: a workshop is organised by Ronan Quarez (Rennes) in Rennes on 24-25 November 2011.

  • 20-24 February 2012: a workshop on Emerging Developments in Real Algebraic Geometry: Positivity, Convexity, NC-Geometry, Optimization is organised by Gennadiy Averkov, Martin Henk (Magdeburg); Salma Kuhlmann, Claus Scheiderer, Markus Schweighofer (Konstanz) in Magdeburg, Germany.

  • Spring 2012: Didier Henrion (Toulouse) and Jerome Malick (Grenoble) are awarded the 2011 Charles Broyden prize for their paper "Projection methods for conic feasibility problems, applications to polynomial sum of squares decompositions" published in Vol. 16, Issue 1, Feb. 2011 of the journal Optimization Method Software.

  • 11-15 June 2012: a school on hyperplane arrangements and related topics is organised by Daniele Faenzi (Pau), Vincent Florens (Pau), Daniel Matei (Bucharest) and Jean Vallès (Pau) in Pau.

  • 27-29 June 2012: Mathieu Claeys, PhD student at LAAS-CNRS, working on semidefinite programming formulations for impulsive optimal control problems, is one of the 5 finalists selected for the student paper award of the American Control Conference, Montreal, Canada.

  • 3-7 September 2012: a summer school on semidefinite optimization is organised by Gabriele Nebe (Aachen) and the Research Training "Group experimental and constructive algebra" funded by the German Research Foundation in Kirchberg/Hunsrueck, Germany.

  • 17-21 September 2012: the Mathematics, Algorithms and Proofs (MAP) conference is organised by Thierry Coquand (Stockholm), Didier Henrion (Toulouse), Henri Lombardi (Besancon), Cordian Riener (Konstanz), Marie-Francoise Roy (Rennes) and Markus Schweighofer (Konstanz) in Konstanz, Germany. The conference includes GeoLMI sessions. See also this poster.

  • 24 February - 2 March 2013: M. Charina (Dortmund), J. B. Lasserre (Toulouse), M. Putinar (Santa Barbara) and J. Stoeckler (Dortmund), organise a workshop on structured function systems and applications at the Mathematisches Forschungsinstitut Oberwolfach, Germany.

  • Summer 2013: J. Fliege (Southampton), J. B. Lasserre (Toulouse), A. N. Letchford (Lancaster) and M. Schweighofer (Konstanz), organise a thematic programme on polynomial optimisation at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.

  • 12-16 November 2013: D. Henrion (Toulouse) and M. Laurent (Amsterdam) organise a conference at the Centre International de Rencontres Mathématiques (CIRM) near Marseille, France.