Abstract
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and inequalities. More precisely, it exploits the optimal solution of a linear relaxation of the problem to compute efficiently a promising upper bound. First experiments on the Coconuts benchmarks demonstrate that this approach is very effective.
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Lebbah, Y., Michel, C., Rueher, M., Daney, D., Merlet, J.-P.: Efficient and safe global constraints for handling numerical constraint systems. SIAM Journal on Numerical Analysis 42(5), 2076–2097 (2004)
Lhomme, O.: Consistency techniques for numeric CSPs. In: Proceedings of IJCAI 1993, Chambéry, France, pp. 232–238 (1993)
Neumaier, A.: Complete search in continuous global optimization and constraint satisfaction. Acta Numerica (2004)
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© 2008 Springer-Verlag Berlin Heidelberg
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Goldsztejn, A., Lebbah, Y., Michel, C., Rueher, M. (2008). Revisiting the Upper Bounding Process in a Safe Branch and Bound Algorithm. In: Stuckey, P.J. (eds) Principles and Practice of Constraint Programming. CP 2008. Lecture Notes in Computer Science, vol 5202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85958-1_49
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DOI: https://doi.org/10.1007/978-3-540-85958-1_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85957-4
Online ISBN: 978-3-540-85958-1
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