no. 5
Linear convergence in the approximation of rank-one convex envelopes
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 811-820

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope f rc of a given function f:ℝ n×m →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 : 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 
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     author = {Bartels, S\"oren},
     title = {Linear convergence in the approximation of rank-one convex envelopes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {811--820},
     year = {2004},
     publisher = {EDP Sciences},
     volume = {38},
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     doi = {10.1051/m2an:2004040},
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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

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