A second-order pruning step for verified global optimization |
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Authors: | Marco Schnurr |
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Institution: | (1) Institute for Applied and Numerical Mathematics, University of Karlsruhe, 76128 Karlsruhe, Germany |
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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.
This paper contains some results from the author’s dissertation 29]. |
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Keywords: | Global optimization Interval analysis Pruning step |
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