A second-order pruning step for verified global optimization

Authors:
Marco Schnurr
Affiliations:
Institute for Applied and Numerical Mathematics, University of Karlsruhe, Karlsruhe, Germany 76128
Venue:
Journal of Global Optimization
Year:
2009

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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.