Comparison of active-set and gradient projection-based algorithms for box-constrained quadratic programming

This paper presents on four chosen benchmarks an experimental evidence of efficiency of active-set-based algorithms and a gradient projection scheme exploiting Barzilai–Borwein-based steplength rule for box-constrained quadratic programming problems, which have theoretically proven rate of convergence. The crucial phase of active-set-based algorithms is the identification of the appropriate active set combining three types of steps—a classical minimization step, a step expanding the active set and a step reducing it. Presented algorithms employ various strategies using the components of the gradient for an update of this active set to be fast, reliable and avoiding undesirable oscillations of active set size.