  We present a method for the steady state optimization of nonlinear delay
differential equations. The method ensures stability and robustness, where a
system is called robust if it remains stable despite uncertain parameters.
Essentially, we ensure stability of all steady states of the nonlinear system
on the steady state manifold that results from the variation of the uncertain
parameters. The uncertain parameters are characterized by finite intervals,
which may be interpreted as error bars and therefore are of immediate practical
relevance. Stability despite uncertain parameters can be guaranteed by
enforcing a lower bound on the distance of the optimal steady state to
submanifolds of saddle-node and Hopf bifurcations on the steady state manifold.
We derive constraints that ensure this distance. The proposed method differs
from previous ones in that stability and robustness are guaranteed with
constraints instead of with the cost function. Because the cost function is not
required to enforce stability and robustness, it can be used to state economic
or similar goals, which is natural in applications. We illustrate the proposed
method by optimizing a laser diode. The optimization finds a steady state of
maximum intensity while guaranteeing asymptotic or exponential stability
despite uncertain model parameters.
