A relaxation procedure for calculating (G–)minimax optimal designs

Summary: In nonlinear statistical models, standard optimality functions for experimentaldesigns depend on the unknown parameters of the model. An appealing and robustconcept for choosing a design is the minimax criterion. However, so far, minimax optimaldesigns have been calculated efficiently under various restrictive conditions only. Weextend an iterative relaxation scheme originally proposed by Shimizu and Aiyoshi (1980)and prove its convergence under very general assumptions which cover a variety of situationsconsidered in experimental design. Application to different specific design criteriais discussed and issues of practical implementation are addressed. First numerical resultssuggest that the method may be very efficient with respect to the number of iterationsrequired.*Supported by a grant from the Deutsche Forschungsgemeinschaft. We are grateful toa referee for his constructive suggestions.