Linear convergence in the approximation of rank-one convex envelopes

Bartels, Sören

doi:10.1051/m2an:2004040

Bartels, Sören

ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 811-820.

Résumé

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope $f^{r c}$ of a given function $f : ℝ^{n \times m} \to ℝ$ , 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.

MR Zbl

DOI : 10.1051/m2an:2004040

Classification : 65K10, 74G15, 74G65, 74N99
Mots-clés : nonconvex variational problem, calculus of variations, relaxed variational problems, rank-1 convex envelope, microstructure, iterative algorithm

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     title = {Linear convergence in the approximation of rank-one convex envelopes},
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     publisher = {EDP-Sciences},
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     zbl = {1083.65058},
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Bartels, Sören. Linear convergence in the approximation of rank-one convex envelopes. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 811-820. doi : 10.1051/m2an:2004040. https://www.numdam.org/articles/10.1051/m2an:2004040/

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