Abstract
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.
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This paper is an extended version of [10] presented at CP 2008 where it has been granted the best research paper award.
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Goldsztejn, A., Granvilliers, L. A new framework for sharp and efficient resolution of NCSP with manifolds of solutions. Constraints 15, 190–212 (2010). https://doi.org/10.1007/s10601-009-9082-3
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DOI: https://doi.org/10.1007/s10601-009-9082-3