A semidefinite programming study of the Elfving theorem
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 ?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
elfving theorem, semidefinite programming, ptimal designs, tangent cones, constraint qualification
3117-3130
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
2011
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Houduo
(2011)
A semidefinite programming study of the Elfving theorem.
Journal of Statistical Planning and Inference, 141, .
(doi:10.1016/j.jspi.2011.03.033).
Abstract
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 ?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
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Published date: 2011
Keywords:
elfving theorem, semidefinite programming, ptimal designs, tangent cones, constraint qualification
Identifiers
Local EPrints ID: 181549
URI: http://eprints.soton.ac.uk/id/eprint/181549
ISSN: 0378-3758
PURE UUID: 8033f286-1232-45d9-8ec9-4befec745a9d
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Date deposited: 19 Apr 2011 13:09
Last modified: 15 Mar 2024 03:21
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