An algorithm based on Semidefinite Programming for finding minimax optimal designs
Please always quote using this URN: urn:nbn:de:0297-zib-66249
- An algorithm based on a delayed constraint generation method for solving semi-infinite programs for constructing minimax optimal designs for nonlinear models is proposed. The outer optimization level of the minimax optimization problem is solved using a semidefinite programming based approach that requires the design space be discretized. A nonlinear programming solver is then used to solve the inner program to determine the combination of the parameters that yields the worst-case value of the design criterion. The proposed algorithm is applied to find minimax optimal designs for the logistic model, the flexible 4-parameter Hill homoscedastic model and the general nth order consecutive reaction model, and shows that it (i) produces designs that compare well with minimax $D-$optimal designs obtained from semi-infinite programming method in the literature; (ii) can be applied to semidefinite representable optimality criteria, that include the common A-, E-,G-, I- and D-optimality criteria; (iii) can tackle design problems with arbitrary linear constraints on the weights; and (iv) is fast and relatively easy to use.
Author: | Belmiro P.M. Duarte, Guillaume Sagnol, Weng Kee Wong |
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Document Type: | ZIB-Report |
Tag: | Cutting plane algorithm; Design efficiency; Equivalence theorem; Model-based optimal design; Nonlinear programming |
MSC-Classification: | 62-XX STATISTICS / 62Kxx Design of experiments [See also 05Bxx] / 62K05 Optimal designs |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C47 Minimax problems [See also 49K35] | |
Date of first Publication: | 2017/12/20 |
Series (Serial Number): | ZIB-Report (18-01) |
ISSN: | 1438-0064 |
Published in: | Computational Statistics & Data Analysis |
DOI: | https://doi.org/10.1016/j.csda.2017.09.008 |