Mardi 7 Mars

Heure:	11:30 - 12:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Valid quadratic inequalities for convex and some non-convex quadratic sets
Description:	Julio César Góez In recent years, the generalization of Balas disjunctive cuts for mixed integer linear optimization problems to mixed integer non-linear optimization problems has received significant attention. Among these studies, mixed integer second order cone optimization (MISOCO) is a special case. For MISOCO one has the disjuncti ve conic cuts approach. That generalization introduced the concept of disjunctive conic cuts (DCCs) and disjunctive cylindrical cuts (DCyCs). Specifically, it showed that under some mild assumptions the intersection of those DCCs and DCyCs with a closed convex set, given as the intersection of a second order cone and an affine set, is the convex hull of the intersection of the same set with a linear disjunction. The key element in that analysis is the use of pencils of quadrics to find close forms for deriving the DCCs and DCyCs. In this talk we present an overview of the DCCs main results and we use the same approach to show the existence of valid conic inequalities for hyperboloids and non-convex quadratic cones when the disjunction is defined by parallel hyperplanes. Joint work with Miguel F. Anjos.