Constrained D- and D1-optimal designs for polynomial regression

In the common polynomial regression model of degree m we consider the problem of determining the D- and D1-optimal designs subject to certain constraints for the D- efficiencies in the models of degree m – j,m + j , … m + k (m > j > 0 k > 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 other hand give an answer to the question of the existence of a design satisfying all constraints. Our approach is based on a combination of general equivalence theory with the theory of canonical moments. In the case of equal bounds for the D1-efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.