  Among the major difficulties that one may encounter when estimating
parameters in a nonlinear regression model are the nonuniqueness of the
estimator, its instability with respect to small perturbations of the
observations and the presence of local optimizers of the estimation criterion.
We show that these estimability issues can be taken into account at the design
stage, through the definition of suitable design criteria. Extensions of $E$-,
$c$- and $G$-optimality criteria are considered, which when evaluated at a
given $\theta ^0$ (local optimal design), account for the behavior of the model
response $\eta(\theta )$ for $\theta$ far from $\theta ^0$. In particular, they
ensure some protection against close-to-overlapping situations where
$\|\eta(\theta )-\eta(\theta ^0)\|$ is small for some $\theta$ far from $\theta
^0$. These extended criteria are concave and necessary and sufficient
conditions for optimality (equivalence theorems) can be formulated. They are
not differentiable, but when the design space is finite and the set $\Theta$ of
admissible $\theta$ is discretized, optimal design forms a linear programming
problem which can be solved directly or via relaxation when $\Theta$ is just
compact. Several examples are presented.
