The author shows that the mixed-weights least-squares (MWLS) algorithm of Rossiter and Kouvaritakis (ibid., vol. 140, p. 243-54, 1993) can be used for the general positive-definite quadratic programming problem under mild assumptions about the feasible set. This also allows one to use the MWLS algorithm for the general linear programming problem. Thus it is concluded that the algorithm deserves wider attention both in the control community (where an increasing range of problems require solutions to quadratic cost functions under inequality constraints) and in the numerical analysis community. The authors also provide a counter example to one of the proofs in the work of Rossiter and Kouvaritakis. Thus, although the convergence properties of the algorithm appear to be good from simulations, more attention to the numerical and convergence properties would be welcome.