Some results on the upper bound of optimal values in interval convex quadratic programming

One of the fundamental problems in interval quadratic programming is to compute the range of optimal values. For minimized problem with equality constraint, computing the upper bound of the optimal values is known to be NP-hard. One kind of the effective methods for computing the upper bound of interval quadratic programming is so called dual method, based on the dual property of the problem. To obtain the exact upper bound, the dual methods require that the duality gap is zero. However, it is not an easy task to check whether this condition is true when the data may vary inside intervals. In this paper, we first present an easy and efficient method for checking the zero duality gap. Then some relations between the exact upper bound and the optimal value of the dual model considered in dual methods are discussed in detail. We also report some numerical results and remarks to give an insight into the dual method’s behavior.