Semismooth Newton methods for variational problems with inequality constraints

GAMM Mitteilungen

Volumn 33, Issue 1, 2010, Pages 8-24

  Hager, Corinna ^a   Wohlmuth, Barbara I ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Complementarity; Inequality constraints; Newton method; Semismooth

Indexed keywords

EID: 77953147392     PISSN: 09367195     EISSN: None     Source Type: Journal    
DOI: 10.1002/gamm.201010002     Document Type: Article

References (47)

1. J. Bear, Dynamics of fluids in porous media (Dover Publications, Inc, New York, 1972).
2. J. Bear and Y. Bachmat, Introduction to modelling of transport phenomena in porous media (Kluwer Academin Publishers, Dordrecht, 1991).
3. C.J. van Duijn, J. Molenaar, and M. de Neef, Transport in Porous Media 21, 71-93 (1995).
4. R. Helmig, Multiphase flow and transport processes in the subsurface (Springer, 1997).
5. S. Hassanizadeh and W. Gray, Water Resources Research 29(10), 3389 -3405 (1993).
6. Y. Achdou and O. Pironneau, Computational methods for option pricing (SIAM, Philadelphia, 2005).
7. F. Black and M. Scholes, J. Pol. Econ. 81, 637-659 (1973).
8. J. Hull, Options, futures, and other derivatives, 6 edition (Prentice Hall, 2006).
9. P. Jaillet, D. Lamberton, and B. Lapeyre, Acta Appl. Math. 21, 263-289 (1990).
10. P. Wilmott, J. Dewynne, and S. Howison, Option pricing: Mathematical models and computation (Oxford Financial Press, Oxford, 1997).
11. C. Eck, J. Jarušek, and M. Krbec, Unilateral contact problems. Variational methods and existence theorems (CRC Press Taylor & Francis Group, Boca Raton, 2005).
12. N. Kikuchi and J. Oden, Contact problems in elasticity: A study of variational inequalities and finite element methods (SIAM Studies in Applied Mathematics 8, Philadelphia, 1988).
13. T. Laursen, Computational contact and impact mechanics (Springer, Berlin Heidelberg, 2002).
14. P. Wriggers, Computational contact mechanics (J. Wiley & Sons Ltd, Chichester, 2002).
15. J. Alberty, C. Carstensen, and D. Zarrabi, Comput. Methods Appl. Mech. Engrg. 171, 175-204 (1999).
16. W. Han and B.D. Reddy, Comput. Mech. Advances 2, 283-400 (1995).
17. W. Han and B.D. Reddy, Plasticity - Mathematical theory and analysis (Springer, New York, 1999).
18. J.C. Simo and T. J.R. Hughes, Computational inelasticity (Springer, Berlin Heidelberg, 1998).
19. F. Facchinei and J.S. Pang, Finite-dimensional variational inequalities and complementary problems (Springer, New York, 2003).
20. R. Glowinski, J.L. Lions, and R. Trémolières, Numerical analysis of variational inequalities (North-Holland, Amsterdam, 1981).
21. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications (SIAM, Philadelphia, 2000).
22. W. Han, S. Jensen, and B.D. Reddy, Numer. Linear Alg. Appl. 4(3), 191-204 (1997).
23. C. Wieners, Z. Angew. Math. Mech. 87(8), 643-660 (2007).
24. S.J. Wright, Primal-dual interior point methods (SIAM, Philadelphia, 1997).
25. J.S. Pang and S.A. Gabriel, Math. Progr. 60, 295-337 (1993).
26. R. Glowinski and P. Le Tallec, Augmented Lagrangian and operator splitting methods in nonlinear mechanics (SIAM Studies in Applied Mathematics 9, Philadelphia, 1989).
27. C. Geiger and C. Kanzow, Theorie und Numerik restringierter Optimierungsaufgaben (Springer, Berlin Heidelberg, 2002).
28. P. Alart and A. Curnier, Comput. Methods Appl. Mech. Engrg. 92, 353-375 (1991).
29. P.W. Christensen, Comput. Methods Appl. Mech. Engrg. 191, 1189-1219 (2002).
30. G. De Saxce and Z.Q. Feng, Mech. Struct. Mach. 19, 301-325 (1991).
31. P. Deuflhard, Newton methods for nonlinear problems - Affine invariance and adaptive algorithms (Springer, Berlin Heidelberg, 2004).
32. M. Hintermüller, K. Ito, and K. Kunisch, SIAM J. Optim. 13(3), 865-888 (2003).
33. B.I. Wohlmuth, SIAM J. Numer. Anal. 38, 989-1012 (2000).
34. S. Hüeber, G. Stadler, and B.I. Wohlmuth, SIAM J. Sci. Comput. 30(2), 572-596 (2008).
35. R. Helmig, A. Weiss, and B.I. Wohlmuth, Comput. Geosci. 13, 373-390 (2009).
36. S. Hassanizadeh, M. Celia, and H. Dahle, Vadose Zone J. 1, 38-57 (2002).
37. P. Binning and M.A. Celia, Advances in Water Resources 22(5), 461-478 (1999).
38. M. de Neef, Modelling capillary effects in heterogeneous porous media, PhD thesis, University of Delft, Netherlands, 2000.
39. R. Huber and R. Helmig, Comput. Geosci. 4, 141-164 (2000).
40. T. Arbogast, L.C. Cowsar, M. F. Wheeler, and I. Yotov, SIAM J. Numer. Anal. 37(4), 1295-1315 (2000).
41. T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov, Multiscale Model. Simul. 6(1), 319-346 (2007).
42. C. Hager, S. Hüeber, and B.I. Wohlmuth, Numerical techniques for the valuation of basket options and its greeks, Tech. Rep. 2008/012, Universität Stuttgart, IANS, 2008, to appear in J. Comput. Fin.
43. B.I. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition (Springer, 2001).
44. C. Hager and B.I. Wohlmuth, Comput. Methods Appl. Mech. Engrg. 198, 3411-3427 (2009).
45. S. Hüeber and B.I. Wohlmuth, SIAM J. Numer. Anal. 43(1), 157-173 (2005).
46. B. Flemisch and B.I. Wohlmuth, Comput. Methods Appl. Mech. Engrg. 196, 1589-1602 (2007).
47. Y. Achdou and O. Pironneau, Appl. Math. Finance 12(3), 201-241 (2005).