  We search saddle points for a large class of convex-concave Lagrangian. A
generalized explicit iterative scheme based on Arrow-Hurwicz method converges
to a saddle point of the problem. We also propose in this work, a convergent
semi-implicit scheme in order to accelerate the convergence of the iterative
process. Numerical experiments are provided for a nontrivial numerical problem
modeling an optimal shape problem of thin torsion rods. This semi-implicit
scheme is figured out in practice robustly efficient in comparison with the
explicit one.
