As interval coefficients may appear in the function we have to define what will be called a minimum or a maximum of . First we assume that there is no interval coefficients in and denote by the minimal or maximal value of over a set of ranges defined for and an accuracy with which we want to determine the extremum. The algorithm will return an interval as an approximation of such that for a minimization problem and for a maximization problem . The algorithm will also return a value for where the extremum occurs. If we deal with a constrained optimization problem we will have:

- or and
- and

If there are interval coefficients in the optimum function there is not a unique but according to the value of the coefficient a minimal extremum value and a maximal extremum value . The algorithm will return in the lower bound of an approximation of and in the upper bound of an approximation of which verify for a minimization problem:

If the optimum function has no interval coefficients the algorithm may return no solution if the interval evaluation of the optimum function has a width larger than . Evidently the algorithm will also return no solution if there is no solution that satisfy all the constraints.