Abstract
The concepts of D-, A- and E-minimax optimality criteria of designs for estimating the slopes of a response surface are considered for situations where the region of interest may not be identical to the experimental region. Optimal second-order designs are derived for the situation where the experimental region and the region of interest are both hyperspherical with a common centre. The dependence of the optimal design on the relative sizes of the regions is investigated. Further, the perfomance of designs optimal for one region in estimating slopes in other regions is also examined.