H1-projection into the set of convex functions : a saddle-point formulation
Carlier, Guillaume; Lachand-Robert, Thomas; Maury, Bertrand (2001), H1-projection into the set of convex functions : a saddle-point formulation, ESAIM. Proceedings, 10, p. 277-289. http://dx.doi.org/10.1051/proc:2001017
TypeArticle accepté pour publication ou publié
Journal nameESAIM. Proceedings
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Abstract (EN)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 on gradient fi elds. It leads in a natural way to an in finite-dimensional saddle-point problem, which can be shown to be ill-posed in general. Existence and uniqueness of a saddle point is obtained for a Lagrangian de ned in suitable spaces. This well-posed formulation does not lead to an implementable algorithm. Yet, numerical experiments based on a discretization of the fi rst formulation exhibit a good behaviour.
Subjects / Keywordssaddle point; Convex functions
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