Constrained D- and D-1-optimal designs for polynomial regression

In the common polynomial regression model of degree m we consider the probl em of determining the D- and D-1-optimal designs subject to certain constra ints for the D-1-efficiencies in the models of degree m - j, m - j + 1..... m + k(m > j greater than or equal to 0, k greater than or equal to 0 given ). We present a complete solution of these problems, which on the one hand allow a fast computation of the constrained optimal designs and on the othe r hand give an answer to the question of the existence of a design satisfyi ng all constraints. Our approach is based on a combination of general equiv alence theory with the theory of canonical moments. In the case of equal bo unds for the D-1-efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal po lynomials.