A semi-smooth Newton method for solving elliptic equations with gradient constraints
ESAIM: Mathematical Modelling and Numerical Analysis (2008)
- Volume: 43, Issue: 2, page 209-238
- ISSN: 0764-583X
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topGriesse, 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
top- J.-M. Bony, Principe du maximum dans les espaces de Sobolev. C. R. Acad. Sci. Paris Sér. A-B265 (1967) 333–336.
- A. Brooks and T. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng.32 (1982) 99–259.
- X. Chen, Superlinear convergence and smoothing quasi-Newton methods for nonsmooth equations. J. Comput. Appl. Math.80 (1997) 105–126.
- M. Delfour and J.-P. Zolésio, Shapes and Geometries. Analysis, Differential Calculus, and Optimization. Philadelphia (2001).
- L.C. Evans, A second order elliptic equation with gradient constraint. Comm. Partial Differ. Equ.4 (1979) 555–572.
- D. Gilbarg and N.S. Trudinger, Elliptic Differential Equations of Second Order. Springer, New York (1977).
- M. Hintermüller and K. Kunisch, Stationary optimal control problems with pointwise state constraints. SIAM J. Optim. (to appear).
- M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim.13 (2002) 865–888.
- H. Ishii and S. Koike, Boundary regularity and uniqueness for an elliptic equation with gradient constraint. Comm. Partial Differ. Equ.8 (1983) 317–346.
- 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.
- C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, Cambridge (1987).
- 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.
- O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations. Academic Press, New York (1968).
- S. Shreve and H.M. Soner, Optimal investment and consumption with transaction costs. Ann. Appl. Probab.4 (1994) 609–692.
- K. Stromberg, Introduction to Classical Real Analysis. Wadsworth International, Belmont, California (1981).
- G. Troianiello, Elliptic Differential Equations and Obstacle Problems. Plenum Press, New York (1987).
- 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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