A New Presolving Technique for Convex Box-Constrained Quadratic Programming Problems

In this paper, we propose a new presolving technique for convex quadratic programming problems with box constraints. The principle is to exploit a logical and simple relationship between variables in order to simplify the original problem as much as possible with little effort. This technique involves fixing certain variables of the problem’s optimal solution at one of their bounds, either lower or upper. A numerical illustrative example is presented, and the numerical experiments have been conducted to evaluate the effectiveness of the proposed technique. The obtained results show that the proposed presolving procedure is very promising and improve significantly computational efficiency of the active-set quadprog algorithm, and the Interior Point quadprog algorithm of the Matlab optimization toolbox