Determining the objective value range for a class of interval convex optimization problems

This paper generalizes a method of determining the objective value range of 2 quadratic programming problems to a general class of interval convex programming ones, where all coefficients in objective function and constraints are interval numbers. The upper bound and lower bound of the objective values of the interval quadratic program is calculated by formulating a pair of two-level mathematical programs. 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 convex programming problem. Solving the pair of convex programs produces the interval of the objective values of the problem. Numerical results confirms the procedure of the presented approach.