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 ×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.


Global Optimization Constraint Satisfaction Interval Arithmetic Simplex Algorithm Opposite Corner 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ignacio Araya
    • 1
  • Gilles Trombettoni
    • 2
  • Bertrand Neveu
    • 3
  1. 1.UTFSMChile
  2. 2.IRIT, INRIA, I3SUniversité Nice-SophiaFrance
  3. 3.Imagine LIGM Université Paris-EstFrance

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