Abstract
We consider pruning steps used in a branch-and-bound algorithm for verified global optimization. A first-order pruning step was given by Ratz using automatic computation of a first-order slope tuple (Ratz, Automatic Slope Computation and its Application in Nonsmooth Global Optimization. Shaker Verlag, Aachen, 1998; J. Global Optim. 14: 365–393, 1999). In this paper, we introduce a second-order pruning step which is based on automatic computation of a second-order slope tuple. We add this second-order pruning step to the algorithm of Ratz. Furthermore, we compare the new algorithm with the algorithm of Ratz by considering some test problems for verified global optimization on a floating-point computer.
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This paper contains some results from the author’s dissertation [29].
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Schnurr, M. A second-order pruning step for verified global optimization. J Glob Optim 44, 349–374 (2009). https://doi.org/10.1007/s10898-008-9331-9
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DOI: https://doi.org/10.1007/s10898-008-9331-9