Determining the Optimal Value Bounds of the Objective Function in Interval Quadratic Programming Problem with Unrestricted Variables in Sign

In the most real-world applications, the parameters of the problem are not well understood. This is caused the problem data to be uncertain and indicated with intervals. Interval mathematical models include interval linear programming and interval nonlinear programming problems.A model of interval nonlinear programming problems for decision making based on uncertainty is interval quadratic programming. These types of problems, in which the parameters are inaccurately expressed, are widely used in various sciences, including inventory management, economics, stock selection, engineering design, and molecular study. Interval parameters in these optimization problems cause the value of the objective function to be inaccurate and interval. There are several methods to compute the optimal bounds of the objective function for interval quadratic programming problems. This article examines the most difficult type of interval quadratic programming problems that includes unrestricted decision variables in sign, and provides a new method for determining the bounds of its objective function. In this method, by solving sub-models that include nonnegative variables, the optimal value bounds of the objective function are obtained.