Taylor Models in Deterministic Global Optimization
Deterministic global optimization requires a global search with rejection of subregions. To reject a subregion, bounds on the range of the constraints and objective function can be used. Although often effective, simple interval arithmetic sometimes gives impractically large bounds on the ranges. However, Taylor models as developed by Berz et al. may be effective in this context. Efficient incorporation of such models in a general global optimization package is a significant project. Here, we use the system COSY Infinity by Berz et al. to study the bounds on the range of various order Taylor models for certain difficult test problems we have previously encountered. Based on that, we conclude that Taylor models may be useful for some, but not all, problems in verified global optimization. Forthcoming improvements in the COSY Infinity interface will help us reach stronger conclusions.
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