φp-optimal designs for a linear log contrast model for experiments with mixtures

A mixture experiment is an experiment in which the k ingredients are nonnegative and subject to the simplex restriction Sigma(k)(i=1) x(i) = 1 on the (k - 1)-dimensional probability simplex Sk-1. In this work, an essentially complete class of designs under the Kiefer ordering for a linear log contrast model with a mixture experiment is presented. Based on the completeness result, phi(p)-optimal designs for all p, -infinity <= p <= 1 including D- and A-optimal are obtained, where the eigenvalues of the design moment matrix are used. By using the approach presented here, we gain insight on how these phi(p)-optimal designs behave.