An implementation of an interior-point algorithm for convex quadratic programming using the identification of superfluous constraints

In this paper quadratic programming problems with strict convex objective functions f and linear constraints are considered. Based on a nonlinear separation theorem, a complete characterization of constraints that are superfluous in an optimal point is given. It allows to derive sufficient conditions for deletion of restrictions. The corresponding conditions can easily be checked if upper bounds on the objective are available. The criteria are implemented within Mehrotra’s primal-dual interior-point algorithm. Numerical results are reported for a various number of randomly generated problem instances. The effect of using one single watchpoint and multiple watchpoints, alternatively, is examined. It turns out that the identification of superfluous constraints is highly efficient in early stages of the solution procedure and leads to a decisive reduction of the problem size.