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Linear convergence in the approximation of rank-one convex envelopes

Published online by Cambridge University Press:  15 October 2004

Sören Bartels
Sören Bartels*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA. sba@math.umd.edu.
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Abstract

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope $f^{rc}$ of a given function $f:\mathbb{R}^{n\times m} \to \mathbb{R}$, i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

Keywords

Nonconvex variational problemcalculus of variationsrelaxed variational problemsrank-1 convex envelopemicrostructureiterative algorithm.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 811 - 820
Copyright
© EDP Sciences, SMAI, 2004

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