A semi-smooth Newton method for solving elliptic equations with gradient constraints

Roland Griesse; Karl Kunisch

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 43, Issue: 2, page 209-238
  • ISSN: 0764-583X

Abstract

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Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.

How to cite

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Griesse, Roland, and Kunisch, Karl. "A semi-smooth Newton method for solving elliptic equations with gradient constraints." ESAIM: Mathematical Modelling and Numerical Analysis 43.2 (2008): 209-238. <http://eudml.org/doc/194449>.

@article{Griesse2008,
abstract = { Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution. },
author = {Griesse, Roland, Kunisch, Karl},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Gradient constraints; active set strategy; regularization; semi-smooth Newton method; primal-dual active set method.; gradient constraints; primal-dual active set method; elliptic equations; numerical examples},
language = {eng},
month = {12},
number = {2},
pages = {209-238},
publisher = {EDP Sciences},
title = {A semi-smooth Newton method for solving elliptic equations with gradient constraints},
url = {http://eudml.org/doc/194449},
volume = {43},
year = {2008},
}

TY - JOUR
AU - Griesse, Roland
AU - Kunisch, Karl
TI - A semi-smooth Newton method for solving elliptic equations with gradient constraints
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/12//
PB - EDP Sciences
VL - 43
IS - 2
SP - 209
EP - 238
AB - Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
LA - eng
KW - Gradient constraints; active set strategy; regularization; semi-smooth Newton method; primal-dual active set method.; gradient constraints; primal-dual active set method; elliptic equations; numerical examples
UR - http://eudml.org/doc/194449
ER -

References

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  12. K. Kunisch and J. Sass, Trading regions under proportional transaction costs, in Operations Research Proceedings, U.M. Stocker and K.-H. Waldmann Eds., Springer, New York (2007) 563–568.  
  13. O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations. Academic Press, New York (1968).  
  14. S. Shreve and H.M. Soner, Optimal investment and consumption with transaction costs. Ann. Appl. Probab.4 (1994) 609–692.  
  15. K. Stromberg, Introduction to Classical Real Analysis. Wadsworth International, Belmont, California (1981).  
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  17. M. Wiegner, The C1,1-character of solutions of second order elliptic equations with gradient constraint. Comm. Partial Differ. Equ.6 (1981) 361–371.  

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