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Solution method for discrete double obstacle problems based on a power penalty approach. (English) Zbl 1499.90256

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90-08 Computational methods for problems pertaining to operations research and mathematical programming
65K15 Numerical methods for variational inequalities and related problems
Full Text: DOI

References:

[1] C. Avramescu, A generalization of Miranda’s theorem, Semin. Fixed Point Theory Cluj-Napoca, 3, 121-127 (2002) · Zbl 1047.47040
[2] O. Bokanowski; S. Maroso; H. Zidani, Some convergence results for Howard’s algorithm, SIAM J. Numer. Anal., 47, 3001-3026 (2009) · Zbl 1201.49030 · doi:10.1137/08073041X
[3] L. A. Caffarelli; R. J. McCann, Free boundaries in optimal transport and Monge-Ampere obstacle problems, Ann. Math., 171, 673-730 (2010) · Zbl 1196.35231 · doi:10.4007/annals.2010.171.673
[4] M. Dai; F. Yi, Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem, J. Differ. Equ., 246, 1445-1469 (2009) · Zbl 1227.35182 · doi:10.1016/j.jde.2008.11.003
[5] J. E. Dennis Jr. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Inc., Englewood Cliffs, NJ, 1983. · Zbl 0579.65058
[6] G. Duvaut and J.-L. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976. · Zbl 0331.35002
[7] D. Han and J. W. L. Wan, Multigrid methods for second order Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs equations, SIAM J. Sci. Comput., 35 (2013), S323-S344. · Zbl 1281.65128
[8] T. Kärkkäinen; K. Kunisch; P. Tarvainen, Augmented Lagrangian active set methods for obstacle problems, J. Optim. Theory Appl., 119, 499-533 (2003) · Zbl 1045.49026 · doi:10.1023/B:JOTA.0000006687.57272.b6
[9] R. Kornhuber, Monotone multigrid methods for elliptic variational inequalities I, Numer. Math., 69, 167-184 (1994) · Zbl 0817.65051 · doi:10.1007/BF03325426
[10] P. Kovalov and V. Linetsky, Valuing convertible bonds with stock price, volatility, interest rate, and default risk, FDIC Center for Financial Research Working Paper Series, 2008.
[11] Y. Peres; O. Schramm; S. Sheffield; D. B. Wilson, Tug-of-war and the infinity Laplacian, J. Amer. Math. Soc., 22, 167-210 (2009) · Zbl 1206.91002 · doi:10.1090/S0894-0347-08-00606-1
[12] Z. Sun; Z. Liu; X. Yang, On power penalty methods for linear complementarity problems arising from American option pricing, J. Glob. Optim., 63, 165-180 (2015) · Zbl 1321.91115 · doi:10.1007/s10898-015-0291-6
[13] S. Wang; X. Yang, A power penalty method for a bounded nonlinear complementarity problem, Optimization, 64, 2377-2394 (2015) · Zbl 1327.90340 · doi:10.1080/02331934.2014.967236
[14] S. Wang; X. Q. Yang; K. L. Teo, Power penalty method for a linear complementarity problem arising from American option valuation, J. Optim. Theory Appl., 129, 227-254 (2006) · Zbl 1139.91020 · doi:10.1007/s10957-006-9062-3
[15] J. H. Witte; C. Reisinger, A penalty method for the numerical solution of Hamilton-Jacobi-Bellman (HJB) equations in finance, SIAM J. Numer. Anal., 49, 213-231 (2011) · Zbl 1233.65064 · doi:10.1137/100797606
[16] K. Zhang; X. Yang, A power penalty method for discrete HJB equations, Optim. Lett., 14, 1419-1433 (2020) · Zbl 1455.90137 · doi:10.1007/s11590-019-01517-7
[17] K. Zhang; X. Q. Yang; S. Wang; K. L. Teo, Numerical performance of penalty method for American option pricing, Optim. Methods Softw., 25, 737-752 (2010) · Zbl 1197.91189 · doi:10.1080/10556780903051930
[18] J.-X. Zhao; S. Wang, An interior penalty approach to a large-scale discretized obstacle problem with nonlinear constraints, Numer. Algorithms, 85, 571-589 (2020) · Zbl 1462.65075 · doi:10.1007/s11075-019-00827-2
[19] Y. Y. Zhou; S. Wang; X. Q. Yang, A penalty approximation method for a semilinear parabolic double obstacle problem, J. Glob. Optim., 60, 531-550 (2014) · Zbl 1304.49025 · doi:10.1007/s10898-013-0122-6
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