Two proportionality based gradient methods for the solution of large convex bound constrained quadratic programming problems, MPRGP (Modified Proportioning with Reduced Gradient Projections) and P2GP (Proportionality-based Two-phase Gradient Projection) are presented and applied to the solution of auxiliary problems in the inner loop of an augmented lagrangian algorithm called SMALBE (Semi-monotonic Augmented Lagrangian for Bound and Equality constraints). The SMALBE algorithm is used to generate the Lagrange multipliers for the equality constraints. The performance of the algorithms is tested on the solution of the discretized contact problems by means of TFETI (Total Finite Element Tearing and Interconnecting).