H1-projection into the set of convex functions : a saddle-point formulation

We investigate numerical methods to approximate the projection-operator from H1 0 into the set of convex functions. We introduce a new formulation of the problem, based gradient fi elds. It leads in a natural way to an in finite-dimensional saddle-point , which can be shown to be ill-posed in general. Existence and uniqueness of saddle point is obtained for a Lagrangian de ned in suitable spaces. This well-posed does not lead to an implementable algorithm. Yet, numerical experiments on a discretization of the fi rst formulation exhibit a good behaviour.