On the LVI-based numerical method (E47 algorithm) for solving quadratic programming problems

In this paper, a numerical method (termed, E47 algorithm) based on linear variational inequalities (LVI) is presented and investigated to solve quadratic programming (QP) problems which are simultaneously subject to linear equality, inequality and bound constraints. Note that such constrained QP problems can be equivalent to linear variational inequalities and then to piecewise-linear projection equations (PLPE). The E47 algorithm is then adapted to solving the resultant PLPE, and thus the optimal numerical solutions to the QP problems are obtained. In addition, the global linear convergence of such an E47 algorithm is proved. The numerical comparison results between such an E47 algorithm and the active set algorithm are further provided. The efficacy and superiority of the presented E47 algorithm for QP solving are substantiated.