Abstract

A new branch-and-prune algorithm for globally solving nonlinear systems is proposed. The pruning technique combines a multidimensional interval Newton method with the constraint satisfaction algorithm HC4 [1]. The main contributions of this paper are the fine-grained interaction between both algorithms which avoids some unnecessary computation,and the description of HC4 in terms of a chain rule for constraints’ projections. Our algorithm is experimentally compared with two global methods from Ratschek and Rokne [17] and from Puget and Van Hentenryck [16] on Ebers and Moll’ circuit design problem [6]. An interval enclosure of the solution with a precision of twelve significant digits is computed in four minutes, providing an improvement factor of five on the same machine.

Citations