Lower subdifferentiability of quadratic forms

In this paper the authors characterize those quadratic functions whose restrictions to a convex set are boundedly lower subdifferentiable and, for the case of closed hyperbolic convex sets, those which are lower subdifferentiable but not boundedly lower subdifferentiable. Once characterized, they will study the applicability of the cutting plane algorithm of Plastria to problems where the objective function is quadratic and boundedly lower subdifferentiable.