Finding the projection onto the intersection of a closed half-space and a variable box

This paper considers the problem of projecting a vector on the intersection of a closed half-space and a variable box. We present a polynomial time algorithm that is based on a parametric approach for finding the explicit formulas for the metric projection. As an application, the proposed algorithm is applied to compute the metric projection over the epigraph of the Ky Fan kk-norm functions. Computational results on large-scale random test problems are also reported in order to evaluate the algorithm and its complexity time.