  We investigate R-optimal designs for multi-response regression models with
multi-factors, where the random errors in these models are correlated. Several
theoretical results are derived for Roptimal designs, including scale
invariance, reflection symmetry, line and plane symmetry, and dependence on the
covariance matrix of the errors. All the results can be applied to linear and
nonlinear models. In addition, an efficient algorithm based on an interior
point method is developed for finding R-optimal designs on discrete design
spaces. The algorithm is very flexible, and can be applied to any
multi-response regression model.
