Detecting Superfluous Constraints in Quadratic Programming by Varying the Optimal Point of the Unrestricted Problem

Abstract

In [3] QP-problems with strict convex objective functions / were investigated in order to detect constraints that are not active at the optimal point x*. It turned out, that simple calculations performed in parallel with an QP-solver allow a decision to delete restrictions from the problem. This might shrink down the problem size during the optimization procedure. These sufficient conditions for non activity could be generalized to the positive semi-definite case (see [4]).

In the present paper it is shown that the techniques presented in [3] allow to get additional possibilities for a deletion of superfluous constraints. For this, the optimal point x ₀ of the unrestricted QP-problem is suitably disturbed within some special set M(f(x*). This set is unknown in advance but a subset A(x ₀) can algorithmically be generated. It is also proved, that x* is a limit point in A(x ₀).