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.
KeywordsInterval analysis Branch and prune algorithm Preconditioned interval Newton Global constraint for under-constrained systems of equations
Unable to display preview. Download preview PDF.
- 1.Benhamou, F., Goualard, F., Granvilliers, L., & Puget, J. F. (1999). Revising hull and box consistency. In International conference on logic programming (pp. 230–244).Google Scholar
- 2.Benhamou, F., McAllister, D., & Van Hentenryck, P. (1994). CLP(Intervals) revisited. In International symposium on logic programming (pp. 124–138).Google Scholar
- 4.Chablat, D., & Wenger, Ph. (1998). Working modes and aspects in fully-parallel manipulator. In IEEE international conference on robotics and automation (pp. 1970–1976). Piscataway: IEEE.Google Scholar
- 5.Collavizza, H., Delobel, F., & Rueher, M. (1999). Comparing partial consistencies. Reliable Computing, 1, 1–16.Google Scholar
- 8.Goldsztejn, A. (2006). A branch and prune algorithm for the approximation of non-linear AE-solution sets. In Proc. of ACM SAC 2006 (pp. 1650–1654).Google Scholar
- 9.Goldsztejn, A. (2008). Sensitivity analysis using a fixed point interval iteration. Technical Report hal-00339377, CNRS.Google Scholar
- 10.Goldsztejn, A., & Granvilliers, L. (2008). A new framework for sharp and efficient resolution of NCSP with manifolds of solution. In Proceedings of CP 2008. LNCS (Vol. 5202/2008, pp. 190–204).Google Scholar
- 11.Goldsztejn, A., & Hayes, W. (2006). Reliable inner approximation of the solution set to initial value problems with uncertain initial value. In Proc. of SCAN 2006.Google Scholar
- 14.Hayes, B. (2003). A lucid interval. American Scientist, 91(6), 484–488.Google Scholar
- 18.Lhomme, O. (1993). Consistency techniques for numeric CSPs. In Proceedings of IJCAI 1993 (pp. 232–238).Google Scholar