  It is well known that solving a (non-convex) quadratic program is NP-hard. We
show that the problem remains hard even if we are only looking for a
Karush-Kuhn-Tucker (KKT) point, instead of a global optimum. Namely, we prove
that computing a KKT point of a quadratic polynomial over the domain $[0,1]^n$
is complete for the class CLS = PPAD$\cap$PLS.
