A New Framework for Sharp and Efficient Resolution of NCSP with Manifolds of Solutions

When numerical CSPs are used to solve systems of n equations with n variables, the preconditioned interval Newton operator plays two key roles: First it allows handling the n equations as a global constraint, hence achieving a powerful contraction. Second it can prove rigorously the existence of solutions. However, none of these advantages can be used for under-constrained systems of equations, which have manifolds of solutions. A new framework is proposed in this paper to extend the advantages of the preconditioned interval Newton to under-constrained systems of equations. This is achieved simply by allowing domains of the NCSP to be parallelepipeds, which generalize the boxes usually used as domains. Keywords Interval analysis

• Type: Conference
• Year: 2008
• Where: CP
• Authors: Alexandre Goldsztejn, Laurent Granvilliers
• Keywords: Artificial Intelligence, CP 2008, Global Constraint, Keywords Interval Analysis, Under-constrained Systems