09.07.2018 14:00 Filipe Goulart Cabral (Federal University of Rio de Janeiro and Operador Nacional do Sistema Elétrico):
The role of extreme points for convex hull operationsMI 02.08.011 (Boltzmannstr. 3, 85748 Garching)
The goal of this talk is to discuss convex optimization methods for non-convex stochastic optimization problems. We aim to present, in a unified way, two results which lie in the core of widely used algorithms for non-convex programming: the classical Balas’s Theorem about the convex hull of union of polyhedra, and the more recent “Blessing of Binary” theorem from Zou, Ahmed and Sun, proving strong duality for stochastic programming with purely binary state variables. A geometrical formulation will be introduced, interpreting both results by means of Cartesian products and projections. This geometrical intuition will be used for describing new models that are amenable to this theory.