The Fritz-John Condition System in Interval Branch and Bound method

Abstract

. The Interval Branch and Bound (IBB) method is a good choice when a rigorous solution is required. This method handles computational errors in the calculations. Few IBB implementations use the Fritz-John (FJ) optimality condition to eliminate non-optimal boxes in a constrained non-linear programming problem. Applying the FJ optimality condition implies solving an interval-valued system of equations. In the best case, the solution is an empty set if the interval box does not contain an optimizer point. Solving this system of equations is complicated or unsuccessful in many cases. This problem can be caused by the interval box being too wide, the defined system of equations containing unnecessary constraints, or the solver being unsuccessful. These unsuccessful attempts have a negative outcome and only increase the computation time. In this study, we propose some modifications to reduce the running time and computational requirements of the Interval Branch and Bound method.