Adaptive grid semidefinite programming for finding optimal designs
| dc.contributor.author | Duarte, Belmiro P.M. | |
| dc.contributor.author | Wong, Weng Kee | |
| dc.contributor.author | Dette, Holger | |
| dc.date.accessioned | 2016-06-28T14:33:05Z | |
| dc.date.available | 2016-06-28T14:33:05Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | We find optimal designs for linear models using a novel algorithm that iteratively combines a Semidefinite Programming (SDP) approach with adaptive grid (AG) techniques. The search space is first discretized and SDP is applied to find the optimal design based on the initial grid. The points in the next grid set are points that maximize the dispersion function of the SDP-generated optimal design using Nonlinear Programming (NLP). The procedure is repeated until a user-specified stopping rule is reached. The proposed algorithm is broadly applicable and we demonstrate its flexibility using (i) models with one or more variables, and (ii) differentiable design criteria, such as A-, D-optimality, and non-differentiable criterion like E-optimality, including the mathematically more challenging case when the minimum eigenvalue of the information matrix of the optimal design has geometric multiplicity larger than 1. Our algorithm is computationally efficient because it is based on mathematical programming tools and so optimality is assured at each stage; it also exploits the convexity of the problems whenever possible. Using several linear models, we show the proposed algorithm can efficiently find both old and new optimal designs. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/35122 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-17169 | |
| dc.language.iso | en | de |
| dc.relation.ispartofseries | Discussion Paper / SFB823;30, 2016 | en |
| dc.subject | adaptive grid | en |
| dc.subject | semidefinite programming | en |
| dc.subject | nonlinear programming | en |
| dc.subject | model-based optimal design | en |
| dc.subject | continuous design | en |
| dc.subject.ddc | 310 | |
| dc.subject.ddc | 330 | |
| dc.subject.ddc | 620 | |
| dc.title | Adaptive grid semidefinite programming for finding optimal designs | en |
| dc.type | Text | de |
| dc.type.publicationtype | workingPaper | de |
| dcterms.accessRights | open access |
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