Constrained optimal designs

The problem combining optimality criteria using constrained optimization techniques is considered. Constraints may be due to some optimality criteria so that the designs satisfying the constraints will have at least the minimal quality that an investigator wishes to maintain. A necessary and sufficient condition similar to Kiefer (Theorem 1, 1974a) is obtained using Fréchet derivatives. Some examples are presented to illustrate some possible applications of the constrained optimality criterion, including Stigler's (1971) C-restricted D-criterion, Lauter's (1976) multiresponse modeling problem and Lee (1987), combination of A- and D-criteria.