Geodesic
Linear convergence in the approximation of rank-one convex envelopes
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 5, pp. 811-820

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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 
@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 },
     pages = {811--820},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     doi = {10.1051/m2an:2004040},
     mrnumber = {2104430},
     zbl = {1083.65058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004040/}
}
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Bartels, Sören. Linear convergence in the approximation of rank-one convex envelopes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 5, pp. 811-820. doi: 10.1051/m2an:2004040

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