UCLA

An algorithm based on a delayed constraint generation method for solving semi-infiniteprograms for constructing minimax optimal designs for nonlinear models is proposed.The outer optimization level of the minimax optimization problem is solved using asemidefinite programming based approach that requires the design space be discretized. Anonlinear programming solver is then used to solve the inner program to determine thecombination 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 consecutivereaction model, and shows that it (i) produces designs that compare well with minimaxD−optimal designs obtained from semi-infinite programming method in the literature;(ii) can be applied to semidefinite representable optimality criteria, that include thecommon A−, E−, G−, I− and D-optimality criteria; (iii) can tackle design problems witharbitrary linear constraints on the weights; and (iv) is fast and relatively easy to use.