@misc{ara-tro-nev-11-aa-tayglop,
  author = {Araya, Ignacio and Trombettoni, Gilles and Neveu, Bertrand},
  title = {Convex Interval {Taylorization} in Constrained Global Optimization},
  howpublished = {Online document},
  url = {http://www-sop.inria.fr/coprin/trombe/publis/xnewton_submitted.pdf}
  year = 2011,
  month = apr,
  note = {Date extracted from PDF properties},
  comment = {Alternative to AA, compares with AA},
  abstract = {Interval taylorisation has been proposed in the sixties by the interval analysis community for relaxing and filtering continuous constraint systems. Unfortunately, it generally produces a nonconvex relaxation of the solution set. A recent interval Branch & Bound for global optimization, called IbexOpt, generates a convex (polyhedral) approximation of the system at each node of the search tree by performing a specific interval taylorization. Following the works by Lin and Stadtherr, the idea is to select a corner of the studied domain/box as expansion point, instead of the usual midpoint. This paper studies how to better exploit this interval convexification. We first show that selecting the corner which produces the tightest relaxation is NP-hard. We then propose a greedy corner selection heuristic, a variant using several corners simultaneously and an interval Newton that iteratively calls this interval convexification. Experiments on a constrained global optimization benchmark highlight the best variants and allow a first comparison with affine arithmetic}
}