Design of optimal multioutput sampling schedules: Computation of gradients and Hessians

The design of optimal sampling schedules in a dynamic experiment is often accomplished by maximization of a scalar function of the Fisher information matrix, using complex optimization algorithms. In this note exact analytic expressions for the gradients and Hessians of two common design criteria (
D
- and
L
-optimality) are derived. The results allow the use of a wealth of efficient gradient search techniques in such designs.