Computing A-optimal and E-optimal designs for regression models via semidefinite programming
Date
2015
Authors
Ye, Jane J.
Zhou, Julie
Zhou, Wenjie
Journal Title
Journal ISSN
Volume Title
Publisher
Communications in Statistics – Simulation and Computation
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 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.
Description
Keywords
A-optimality, E-optimality, nonlinear regression, SeDuMi, semidefinite programming, trigonometric regression
Citation
Ye, 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.