Wednesday, September 27
Minisymposium 10: New hierarchies of SDP relaxations for polynomial systems
Time: 10:30 - 12:30
Room: L1.201, Building L
Chair 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.
Speakers:
10:30 - 11:00 | Victor Magron (CNRS Verimag Grenoble) Interval enclosures of upper bounds of round off errors using semidefinite programming |
11:00 - 11:30 | Marcelo Forets (Université Grenoble Alpes) Semidefinite characterization of invariant measures for polynomial systems |
11:30 - 12:00 | Tillmann Weisser (LAAS-CNRS) Solving nearly-sparse polynomial optimization problems |
12:00 - 12:30 | Cedric Josz (INRIA) Moment/sum-of-squares hierarchy for complex polynomial optimization |