D-Optimal Designs: A Mathematical Programming Approach Using Cyclotomic Cosets

Article type: Research Article

Authors: Syed, Mujahid N. | Kotsireas, Ilias S. | Pardalos, Panos M.

Affiliations: University of Florida, Department of Industrial and Systems Engineering, 303 Weil Hall, P.O. Box 116595, Gainesville, FL 32611-6595, e-mail: smujahid@ufl.edu, pardalos@ufl.edu | Wilfrid Laurier University, Department of Physics and Computer Science, University Avenue West Waterloo, Ontario N2L 3C5, Canada, e-mail: ikotsire@wlu.ca

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.

Keywords: D-optimal design, cyclotomy cosets, mathematical programming

Journal: Informatica, vol. 22, no. 4, pp. 577-587, 2011