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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  10. K. Ito and K. Kunisch, The primal-dual active set method for nonlinear optimal control problems with bilateral constraints. SIAM J. Contr. Opt.43 (2004) 357–376.  Zbl1077.90051
  11. C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, Cambridge (1987).  Zbl0628.65098
  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.  Zbl1209.91149
  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.  Zbl0813.60051
  15. K. Stromberg, Introduction to Classical Real Analysis. Wadsworth International, Belmont, California (1981).  Zbl0454.26001
  16. G. Troianiello, Elliptic Differential Equations and Obstacle Problems. Plenum Press, New York (1987).  Zbl0655.35002
  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.  Zbl0458.35035

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