Revisiting the Upper Bounding Process in a Safe Branch and Bound Algorithm
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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