Numerical procedure to approximate a singular optimal control problem
Silvia C. Di Marco; Roberto L.V. González
ESAIM: Mathematical Modelling and Numerical Analysis (2007)
- Volume: 41, Issue: 3, page 461-484
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- G. Barles and P.E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal.4 (1991) 271–283.
- M.J. Brooks and K.P. Horn, Shape from shading. MIT Press, Cambridge, MA (1989).
- F. Camilli and L. Grüne, Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. SIAM J. Num. Anal.38 (2000) 1540–1560.
- F. Camilli and A. Siconolfi, Maximal subsolutions for a class of degenerate Hamilton-Jacobi problems. Indiana Univ. Math. J.48 (1999) 271–283.
- E. Cristiani and M. Falcone, Fast semi-Lagrangian schemes for the eikonal equation and applications. http://cpde.iac.rm.cnr.it/file_ uploaded/EFX30053.pdf.
- S.C. Di Marco and R.L.V. González, Minimax optimal control problems. Numerical analysis of the finite horizon case. ESAIM: M2AN33 (1999) 23–54.
- S.C. Di Marco and R.L.V. González, Numerical approximation of a singular optimal control problem. Anales de Simposio Argentino en Investigación Operativa, 32° Jornadas Argentinas de Informática e Investigación Operativa, Sociedad Argentina de Informática e Investigación Operativa (2003).
- S.C. Di Marco and R.L.V. González, Penalization methods in the numerical solution of the eikonal equation. Mecánica Computacional, Vol XXII, ISSN 1666–6070 (2003).
- H. Ishii and M. Ramaswamy, Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Comm. Partial Diff. Eq.20 (1995) 2187–2213.
- P.-L. Lions, E. Rouy and A. Tourin, Shape from shading, viscosity solutions and edges. Numer. Math.64 (1993) 323–353.
- J. Sethian, Fast marching methods. SIAM Rev.41 (1999) 199–235.
- H. Whitney, A function not constant on a connected set of critical points. Duke Math. J.1 (1935) 514–517.