We describe the MPGP (modified proportioning with gradient projection) algorithm for solving quadratic programming problems with separable constraints. The algorithm combines the conjugate gradient steps to minimize the cost function in the face with gradient projection steps to change the face. The decision on which step to use depends on violating the KKT conditions. The MPGP algorithm enjoys the R-linear rate of convergence of both the cost function and norm of projected gradient. We also present an alternative PBBF algorithm using projected Barzilai–Borwein steps with fallback. The performance of the algorithms, including scalability, is illustrated by solving a contact problem with anisotropic Coulomb friction.