MINIMIZATION OF QUADRATIC FUNCTIONS ON CONVEX SETS WITHOUT ASYMPTOTES

Juan Enrique Martinez-Legaz † , Dominikus Noll (1) , Wilfredo Sosa

1 IMT - Institut de Mathématiques de Toulouse UMR5219

The classical Frank and Wolfe theorem states that a quadratic function which is bounded below on a convex polyhedron P attains its infimum on P. We investigate whether more general classes of convex sets F can be identified which have this Frank-and-Wolfe property. We show that the intrinsic characterizations of Frank-and-Wolfe sets hinge on asymptotic properties of these sets.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Juan Enrique Martinez-Legaz †, Dominikus Noll, Wilfredo Sosa. MINIMIZATION OF QUADRATIC FUNCTIONS ON CONVEX SETS WITHOUT ASYMPTOTES. Journal of Convex Analysis, 2018. ⟨hal-01868609⟩