An algorithm based on semidefinite programming for finding minimax optimal designs - Duarte, Belmiro P.M.; Sagnol, Guillaume; Wong, Weng Kee (Computational statistics & data analysis, 2018)
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. •An algorithm for finding continuous minimax optimal designs of experiments for semidefinite representable criteria.•An algorithm based on sequential cutting plane approach.•Semidefinite programming used to find optimal designs on a previously discretized domain.•Nonlinear programming used to find the least attainable parameter combination for local designs.•Algorithm convergence is theoretically demonstrated.