A Branch and Prune Algorithm for the Approximation of Non-Linear AE-Solution Sets

Non-linear AE-solution sets are a special case of parametric systems of equations where universally quantified param-eters appear first. They allow to model many practical situations. A new branch and prune algorithm dedicated to the approximation of non-linear AE-solution sets is pro-posed. It is based on a new generalized interval (intervals whose bounds are not constrained to be ordered) paramet-ric Hansen-Sengupta operator. In spite of some restrictions on the form of the AE-solution set which can be approx-imated, it allows to solve problems which were before out of reach of previous numerical methods. Some promising experimentations are presented