Vendredi 28 Novembre

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Vendredi 28 Novembre
Heure: 11:00 - 12:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: New applications of moment-SOS hierarchies
Description: Victor Magron Semidefinite programming is relevant to a wide range of mathematic fields, including combinatorial optimization, control theory, matrix completion. In 2001, Lasserre introduced a hierarchy of semidefinite relaxations for particular polynomial instances of the Generalized Moment Problem (GMP). My talk emphasizes new applications of this moment-SOS hierarchy, investigated during my PhD and Postdoc research.

In the context of formal proofs for nonlinear optimization, one can combine the moment-SOS hierarchy with maxplus approximation of semiconvex functions. Such a framework is mandatory for formal certification of nonlinear inequalities, occurring by thousands in the proof of Kepler Conjecture by Hales.

I also present how to approximate, as closely as desired, the Pareto curve associated with bicriteria polynomial optimization problems or the projections of semialgebraic sets. For each problem, one builds a hierarchy of semidefinite programs, so that the sequence of bounds converges in L1 norm.

Finally, this hierarchy allows to analyze programs containing loop invariants with polynomial assignments.