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 highdimensional 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 hyperrectangle, 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 twodimensional regions, socalled 2dspaces, that are enclosed by polygons. 2dspaces serve as target regions for pairs of variables and are independent of other 2dspaces. A numerical algorithm for nonlinear problems is presented that is based on iterative MonteCarlo 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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