Linear convergence in the approximation of rank-one convex envelopes

Bartels, Sören

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 $f:{ℝ}^{n\times m}\to ℝ$, 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.

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