D-Optimal Designs: A Mathematical Programming Approach Using Cyclotomic Cosets
Volume 22, Issue 4 (2011), pp. 577–587
Pub. online: 1 January 2011
Type: Research Article
Received
1 July 2011
1 July 2011
Accepted
1 September 2011
1 September 2011
Published
1 January 2011
1 January 2011
Abstract
In this paper, a novel approach involving the concepts from mathematical programming and number theory is proposed to find the D-optimal designs. In specific, we will propose a mathematical formulation for the D-optimal design. In addition to that, we will present the use of cyclotomic cosets in the mathematical formulation, in order to reduce the total number of binary variables. We will illustrate the validity of our proposed method by solving a difficult known instance (N=126) of the D-optimal design.