Publication: An algorithm based on semidefinite programming for finding minimax optimal designs
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An algorithm based on semidefinite programming for finding minimax optimal designs

- Article in a journal -
 

Area
Optimization

Author(s)
Belmiro P. M. Duarte , Guillaume Sagnol , Weng Kee Wong

Published in
Computational Statistics & Data Analysis

Year
2018

Abstract
Abstract 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.

AD Tools
ADiMat

BibTeX
@ARTICLE{
         Duarte2018Aab,
       title = "An algorithm based on semidefinite programming for finding minimax optimal designs",
       journal = "Computational Statistics \& Data Analysis",
       pages = "99--117",
       issn = "0167-9473",
       doi = "https://doi.org/10.1016/j.csda.2017.09.008",
       url = "http://www.sciencedirect.com/science/article/pii/S0167947317302086",
       author = "Belmiro P.M. Duarte and Guillaume Sagnol and Weng Kee Wong",
       keywords = "Cutting plane algorithm, Design efficiency, Equivalence theorem, Model-based
         optimal design, Nonlinear programming",
       abstract = "Abstract 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.",
       volume = "119",
       year = "2018",
       ad_area = "Optimization",
       ad_tools = "ADiMat"
}


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