A semidefinite programming study of the Elfving theorem

The theorem of Elfving is one of the most important and earliest results which have led to the theory of optimal design of experiments. This paper presents a fresh study of it from the viewpoint of modern semidefinite programming. There is one-to-one correspondence between solutions of the derived semidefinite programming problem (SDP) and c-optimal designs. We also derive a uniqueness theorem which ensures a unique optimal design without assuming the linear independence property over the largest set of supporting points. The SDP can also be cast as an ℓ 1 ‐ convex program which has recently been extensively studied and often yields sparse solutions. Our numerical experiments on the trigonometric regression model confirm that the SDP does produce a sparse optimal design.