Newton's method for class of weakly singular optimal control problems

Newton's method for optimal control of highly nonlinear partial differential equations is analyzed using a 2-norm technique. We consider the case where neither the linearization of the equality constraint e characterizing the differential equation is surjective nor a second order sufficient optimality condition holds for the topology on which e is well defined. Such problems occur, for instance, in optimal control of semilinear elliptic equations or for parameter estimation problems. Despite the above mentioned difficulties, sufficient conditions for second order convergence are obtained.