P. Guillaume et M. Masmoudi, NUMERICAL COMPUTATION OF HIGHER-ORDER DER IVATIVES IN SHAPE OPTIMIZATION, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 316(10), 1993, pp. 1091-1096
We show in this paper that it is possible to obtain a good approximati
on of the higher order derivatives in shape optimization problems. Thi
s makes particularly interesting the use of automatic differentiation,
and encouraging numerical results have been derived.