  In this work, a class of parabolic economic optimal control problems is
considered. These problems are characterized by pointwise state constraints
regularized by a parameter, which transforms the pure state constraints in
mixed control-state ones. However, the convergence of classical (semismooth)
Newton methods deteriorates for decreasing values of the regularization
parameter. To tackle this problem, a nonlinear preconditioner is introduced.
This is based on an overlapping optimized waveform-relaxation method
characterized by Robin transmission conditions. Numerical experiments show that
appropriate choices of the overlap and of the Robin parameter lead to a
preconditioned Newton method with a robust convergence against the state
constraints regularization parameter.
