  We give a new characterization of Elfving's (1952) method for computing
c-optimal designs in k dimensions which gives explicit formulae for the k
unknown optimal weights and k unknown signs in Elfving's characterization. This
eliminates the need to search over these parameters to compute c-optimal
designs, and thus reduces the computational burden from solving a family of
optimization problems to solving a single optimization problem for the optimal
finite support set. We give two illustrative examples: a high dimensional
polynomial regression model and a logistic regression model, the latter showing
that the method can be used for locally optimal designs in nonlinear models as
well.
