Ye, Jane J.Zhou, JulieZhou, Wenjie2016-06-282016-06-2820152015Ye, J.J., Zhou, J., & Zhou, W. (2015). Computing A-optimal and E-optimal designs for regression models via semidefinite programming. Communications in Statistics – Simulation and Computation.http://dx.doi.org/10.1080/03610918.2015.1030414http://hdl.handle.net/1828/7382In 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 paper, 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 non-linear 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.enA-optimalityE-optimalitynonlinear regressionSeDuMisemidefinite programmingtrigonometric regressionPostprint