MINIMAX SECOND-ORDER DESIGNS OVER CUBOIDAL REGIONS FOR THE DIFFERENCE BETWEEN TWO ESTIMATED RESPONSES

Minimization of the variance of the difference between estimated responses at two points, maximized over all pairs of points in the factor space, is taken as the design criterion. Optimal designs under this criterion are derived, via a combination of algebraic and numerical techniques, for the full second-order regression model over cuboidal regions. Use of a convexity argument and a surrogate objective function significantly reduces the computational burden.