When a function f is monotonic w.r.t. a variable in a given domain, it is well-known that the monotonicity based interval extension of f computes a sharper image than the natural interval extension does. This paper presents a so-called "occurrence grouping" interval extension [f]og of a function f. When f is not monotonic w.r.t. a variable x in the given domain [B], we try to transform f into a new function fog that is monotonic in two subsets xa and xb of the occurrences of x. fog is increasing w.r.t. xa and decreasing w.r.t. xb. [f] og is the interval extension by monotonicity of fog and produces a sharper interval image than the natural extension does. For finding a good occurrence grouping, we propose a linear program and an algorithm that minimize a Taylor-based overestimation of the image diameter of [f]og. Finally, experiments show the benefits of this new interval extension for solving systems of equations.
|Translated title of the contribution||A new extension of the functions at intervals based on the occurrence grouping|
|Number of pages||10|
|State||Published - 1 Dec 2010|
|Event||Sixiemes Journees Francophones de Programmation par Contraintes, JFPC 2010 - 6th French Speaking Conference on Constraint Programming, JFPC 2010 - Caen, France|
Duration: 9 Jun 2010 → 11 Jun 2010
|Period||9/06/10 → 11/06/10|