The core of this chapter is the description and analysis of the MPRGP (modified proportioning with reduced gradient projection) algorithm for solving bound-constrained quadratic programming problems. This active-set-based algorithm expands the active set by the free gradient projection and carries out minimization in the face by the conjugate gradient method. The algorithm balances the norms of the free and chopped gradients to ensure that the reduced free gradient is always sufficiently large in the CG iterations. The modified algorithm enjoys the R-linear rate of convergence of both the cost function and norm of projected gradient. Moreover, it has the finite termination property even for dual degenerate QP problems. We show that conjugate projector preconditioning (deflation) can improve the convergence rate. We also show how to adapt MPRGP to solve problems with SPS Hessian. The performance of the algorithms, including scalability, is illustrated by solving academic benchmarks and particle simulation.