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Approximating solution spaces as a product of polygons

Harbrecht, Helmut and Tröndle, Dennis and Zimmermann, Markus. (2019) Approximating solution spaces as a product of polygons. Preprints Fachbereich Mathematik, 2019 (13).

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Abstract

Solution spaces are regions of good designs in a potentially high-dimensional design space. Good designs satisfy by definition all requirements that are imposed on them as mathematical constraints. In previous work, the complete solution space was approximated by a hyper-rectangle, i.e., the Cartesian product of permissible intervals for design variables. These intervals serve as independent target regions for distributed and separated design work. For a better approximation, i.e., a larger resulting solution space, this article proposes to compute the Cartesian product of two-dimensional regions, so-called 2d-spaces, that are enclosed by polygons. 2d-spaces serve as target regions for pairs of variables and are independent of other 2d-spaces. A numerical algorithm for non-linear problems is presented that is based on iterative Monte-Carlo sampling.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Tröndle, Dennis
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:05 Dec 2019 15:55
Deposited On:05 Dec 2019 15:55

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