Título: Valid inequalities for quadratic problems via non-expansive functions
Abstract: In 1971, Balas introduced intersection cuts as a method for generating cutting planes in integer optimization. These cuts are derived from convex S-free sets, and inclusion-wise maximal S-free sets yield the strongest intersection cuts. When S is a lattice, maximal S-free sets are well-studied. In this talk, we focus on the case when S is defined by a homogeneous quadratic inequality and provide a partial characterization of maximal S-free polyhedra. Our characterization builds a novel connection between maximality of S-free sets and non-expansive functions between unit spheres.