Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 5, page 811-820
  • ISSN: 0764-583X

Abstract

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A linearly convergent iterative algorithm that approximates the rank-1 convex envelope  f r c 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.

How to cite

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Bartels, Sören. "Linear convergence in the approximation of rank-one convex envelopes." ESAIM: Mathematical Modelling and Numerical Analysis 38.5 (2010): 811-820. <http://eudml.org/doc/194241>.

@article{Bartels2010,
abstract = { A linearly convergent iterative algorithm that approximates the rank-1 convex envelope $f^\{rc\}$ of a given function $f:\mathbb\{R\}^\{n\times m\} \to \mathbb\{R\}$, 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. },
author = {Bartels, Sören},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonconvex variational problem; calculus of variations; relaxed variational problems; rank-1 convex envelope; microstructure; iterative algorithm.; nonconvex variational problem; rank-one convex envelope; phase transitions; crystalline solids; algorithm; convergence; numerical experiments},
language = {eng},
month = {3},
number = {5},
pages = {811-820},
publisher = {EDP Sciences},
title = {Linear convergence in the approximation of rank-one convex envelopes},
url = {http://eudml.org/doc/194241},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Bartels, Sören
TI - Linear convergence in the approximation of rank-one convex envelopes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 5
SP - 811
EP - 820
AB - A linearly convergent iterative algorithm that approximates the rank-1 convex envelope $f^{rc}$ of a given function $f:\mathbb{R}^{n\times m} \to \mathbb{R}$, 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.
LA - eng
KW - Nonconvex variational problem; calculus of variations; relaxed variational problems; rank-1 convex envelope; microstructure; iterative algorithm.; nonconvex variational problem; rank-one convex envelope; phase transitions; crystalline solids; algorithm; convergence; numerical experiments
UR - http://eudml.org/doc/194241
ER -

References

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