Computing maximin efficient experimental designs using the methods of semidefinite programming

摘要

In the paper, we solve the problem of computing the maximin efficient design with respect to the class of all orthogonally invariant criteria. It turns out that on a finite experimental domain, the maximin efficient design can be computed by the methods of semidefinite programming. Using this approach, we can deal with the non-differentiability inherent in the problem, due to which the standard iterative procedures cannot be applied. We illustrate the results on the models of polynomial regression on a line segment and quadratic regression on a cube.