TY - GEN

T1 - A contractor based on convex interval Taylor

AU - Araya, Ignacio

AU - Trombettoni, Gilles

AU - Neveu, Bertrand

PY - 2012

Y1 - 2012

N2 - Interval Taylor has been proposed in the sixties by the interval analysis community for relaxing continuous non-convex constraint systems. However, it generally produces a non-convex relaxation of the solution set. A simple way to build a convex polyhedral relaxation is to select a corner of the studied domain/box as expansion point of the interval Taylor form, instead of the usual midpoint. The idea has been proposed by Neumaier to produce a sharp range of a single function and by Lin and Stadtherr to handle n x n (square) systems of equations. This paper presents an interval Newton-like operator, called X-Newton, that iteratively calls this interval convexification based on an endpoint interval Taylor. This general-purpose contractor uses no preconditioning and can handle any system of equality and inequality constraints. It uses Hansen's variant to compute the interval Taylor form and uses two opposite corners of the domain for every constraint. The X-Newton operator can be rapidly encoded, and produces good speedups in constrained global optimization and constraint satisfaction. First experiments compare X-Newton with affine arithmetic.

AB - Interval Taylor has been proposed in the sixties by the interval analysis community for relaxing continuous non-convex constraint systems. However, it generally produces a non-convex relaxation of the solution set. A simple way to build a convex polyhedral relaxation is to select a corner of the studied domain/box as expansion point of the interval Taylor form, instead of the usual midpoint. The idea has been proposed by Neumaier to produce a sharp range of a single function and by Lin and Stadtherr to handle n x n (square) systems of equations. This paper presents an interval Newton-like operator, called X-Newton, that iteratively calls this interval convexification based on an endpoint interval Taylor. This general-purpose contractor uses no preconditioning and can handle any system of equality and inequality constraints. It uses Hansen's variant to compute the interval Taylor form and uses two opposite corners of the domain for every constraint. The X-Newton operator can be rapidly encoded, and produces good speedups in constrained global optimization and constraint satisfaction. First experiments compare X-Newton with affine arithmetic.

UR - http://www.scopus.com/inward/record.url?scp=84861435415&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-29828-8_1

DO - 10.1007/978-3-642-29828-8_1

M3 - Conference contribution

AN - SCOPUS:84861435415

SN - 9783642298271

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 16

BT - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems - 9th International Conference, CPAIOR 2012, Proceedings

Y2 - 28 May 2012 through 1 June 2012

ER -