A numerical solution method to interval quadratic programming

Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the interval quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides, are represented by interval data. Since the parameters are interval-valued, the objective value is interval-valued as well. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the interval quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into conventional one-level quadratic program. Solving the pair of quadratic programs produces the interval of the objective values of the problem. An example illustrates the whole idea and sheds some light on interval quadratic programming.