Computing A-optimal and E-optimal designs for regression models via semidefinite programming

Abstract

In semidefinite programming (SDP), we minimize a linear objective function subject to a linear matrix being positive semidefinite. A powerful program, SeDuMi, has been developed in MATLAB to solve SDP problems. In this article, we show in detail how to formulate A-optimal and E-optimal design problems as SDP problems and solve them by SeDuMi. This technique can be used to construct approximate A-optimal and E-optimal designs for all linear and nonlinear regression models with discrete design spaces. In addition, the results on discrete design spaces provide useful guidance for finding optimal designs on any continuous design space, and a convergence result is derived. Moreover, restrictions in the designs can be easily incorporated in the SDP problems and solved by SeDuMi. Several representative examples and one MATLAB program are given.

KEYWORDS:

• A-optimality
• E-optimality
• Nonlinear regression
• SeDuMi
• Semidefinite programming
• Trigonometric regression

MATHEMATICS SUBJECT CLASSIFICATION:

• MSC 2010
• 62K05
• 62K20

Acknowledgments

This research work is supported by Discovery Grants from the Natural Science and Engineering Research Council of Canada. The authors would like to thank the referees for their helpful comments and suggestions.