Linear convergence in the approximation of rank-one convex envelopes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, p. 811-820

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

DOI : https://doi.org/10.1051/m2an:2004040
Classification:  65K10,  74G15,  74G65,  74N99
Keywords: nonconvex variational problem, calculus of variations, relaxed variational problems, rank-1 convex envelope, microstructure, iterative algorithm
@article{M2AN_2004__38_5_811_0,
author = {Bartels, S\"oren},
title = {Linear convergence in the approximation of rank-one convex envelopes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {5},
year = {2004},
pages = {811-820},
doi = {10.1051/m2an:2004040},
zbl = {1083.65058},
mrnumber = {2104430},
language = {en},
url = {http://www.numdam.org/item/M2AN_2004__38_5_811_0}
}

Bartels, Sören. Linear convergence in the approximation of rank-one convex envelopes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, pp. 811-820. doi : 10.1051/m2an:2004040. http://www.numdam.org/item/M2AN_2004__38_5_811_0/

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