Non-linear Global Optimization using Interval Arithmetic and Constraint Propagation

In this Chapter a new branch-and-bound method for global optimization is presented. The method combines the classical interval global optimization method with constraint propagation techniques. The latter is used for including solutions of the necessary condition f'(x)=0. The constraint propagation is implemented as an extension of the automatic differentiation library FADBAD, which implements forward and backward differentiation. Thus the user of the integrated programme only has to implement the function expression. For illustration purposes the performance is illustrated through a couple of numerical examples.