Vendredi 28 Novembre
Heure: 
11:00  12:30 
Lieu: 
Salle B107, bâtiment B, Université de Villetaneuse 
Résumé: 
New applications of momentSOS 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 momentSOS hierarchy, investigated during my PhD and Postdoc research.
In the context of formal proofs for nonlinear optimization, one can combine the momentSOS 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. 

