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Wednesday, September 27

Minisymposium 10: New hierarchies of SDP relaxations for polynomial systems

Time: 10:30 - 12:30
Room: L1.201, Building L
and Organiser: Victor Magron, CNRS Verimag Grenoble

Semidefinite programming (SDP) is relevant to a wide range of mathematical fields, including continuous optimization, control theory, matrix completion. In 2001, Lasserre introduced a hierarchy of SDP relaxations for approximating polynomial infima.

The topics of this minisymposium emphasizes new applications of SDP hierarchies to address specific problems in the following fields:

  • floating-point arithmetics, by providing interval enclosures for upper bounds of roundoff errors;
  • dynamical systems, by characterizing invariant measures of polynomial maps, in both discrete-time and continuous-time settings;
  • nearly sparse polynomial optimization, by providing a sparsity-adapted hierarchy for problems with constraints satisfying almost always a certain sparsity pattern;
  • electric power systems, by providing a complex moment/sum-of-squares hierarchy also able to exploit sparsity.



10:30 - 11:00Victor Magron (CNRS Verimag Grenoble)
Interval enclosures of upper bounds of round off errors using semidefinite programming
11:00 - 11:30Marcelo Forets (Université Grenoble Alpes)
Semidefinite characterization of invariant measures for polynomial systems
11:30 - 12:00Tillmann Weisser (LAAS-CNRS)
Solving nearly-sparse polynomial optimization problems
12:00 - 12:30Cedric Josz (INRIA)
Moment/sum-of-squares hierarchy for complex polynomial optimization



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