I study set programming: the computation of sets satisfying given properties and maximizing some criteria like their volume. Various techniques can be employed depending on the family of sets considered:
Polyhedral computation or dual dynamic programming for polyhedra,
Semidefinite programming for ellipsoids and
Sum-of-Squares programming for sublevel sets of polynomials or sets with polynomial support function.
I am also interested in the computation of infeasibility certificates for set programs. I apply set programming to the stability analysis and control synthesis of hybrid systems and to the approximation of the Entropic Cone.
Benoît Legat is a postdoctoral associate at MIT with Prof. Pablo Parrilo in the Laboratory for Information and Decision Systems (LIDS). He received his Ph.D. degree in applied mathematics from the UCLouvain, Belgium, in 2020. His research interests include mathematical optimization, invariant set computation and optimal control.CV