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Non Convergence Result for Conformal Approximation of Variational Problems Subject to a Convexity Constraint

Philippe Choné (chone***at***ensae.fr)
Hervé Le Meur (Herve.LeMeur***at***math.u-psud.fr)

Abstract: In this article, we are interested in the minimization of functionals in the set of convex functions. We investigate the discretization of the convexity through various numerical methods and find a geometrical obstruction confirmed by numerical simulations. We prove that there exist some convex functions that cannot be the limit of any conformal $P_1$ Finite Element sequence for a wide variety of refined meshes.

Keywords: convexity, finite elements, interpolation, conformal approximation, minimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: accepted in Numerical Functional Analysis and Optimization

Download: [Postscript][Compressed Postscript]

Entry Submitted: 01/22/2001
Entry Accepted: 01/28/2001
Entry Last Modified: 01/22/2001

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