A semidefinite programming study of the Elfving theorem

作者：Qi Houduo^*

来源：Journal of Statistical Planning and Inference, 2011, 141(9): 3117-3130.

DOI：10.1016/j.jspi.2011.03.033

• Elfving theorem
• Semidefinite programming
• Optimal designs
• Tangent cones
• Constraint qualification

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.

• 出版日期2011-9