An algorithm based on semidefinite programming for finding minimax optimal designs

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)99-117
Number of pages19
JournalComputational Statistics and Data Analysis
Volume119
DOIs
Publication statusPublished - 2018 Mar

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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