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 parameters 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 proposed. It is based on a new generalized interval (intervals whose bounds are not constrained to be ordered) parametric Hansen-Sengupta operator. In spite of some restrictions on the form of the AE-solution set which can be approximated, it allows to solve problems which were before out of reach of previous numerical methods. Some promising experimentations are presented. Categories and Subject Descriptors G.1 [Numerical Analysis]: Miscellaneous General Terms Theory, Algorithms Keywords AE-solution set, branch and prune, Hansen-Sengupta, generalized intervals.

• Type: Conference
• Year: 2006
• Where: SAC
• Authors: Alexandre Goldsztejn
• Keywords: Ae-solution Set, Applied Computing, Generalized Intervals, Non-linear Ae-solution Sets, SAC 2006