Are all quadratic programming problems necessarily convex? As far as I know, the general QP (P) as min 1/2 x^TQx + c^Tx s.t. linear constraints is convex iff the Q (Hessian) is positive semi-definite.
No, QP problems aren't necessarily convex. It is correct that Q must be positive semidefinite(PSD). This is the case here; the matrix S (at time 36:10) is certainly PSD by construction. Hence this is a convex quadratic program, with a solution guaranteed if the KKT theorem holds.
