An algorithm based on semidefinite programming for finding minimax optimal designs

Belmiro P.M. Duarte, Guillaume Sagnol and Weng Kee Wong

Computational Statistics & Data Analysis, 2018, vol. 119, issue C, 99-117

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.

Keywords: Cutting plane algorithm; Design efficiency; Equivalence theorem; Model-based optimal design; Nonlinear programming (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:119:y:2018:i:c:p:99-117

DOI: 10.1016/j.csda.2017.09.008

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