A. Alla, M. Falcone, and D. Kalise, An Efficient Policy Iteration Algorithm for Dynamic Programming Equations, SIAM Journal on Scientific Computing, vol.37, issue.1, pp.181-200, 2015.
DOI : 10.1137/130932284
URL : https://hal.archives-ouvertes.fr/hal-01068295

W. Alt and C. Schneider, Linear-quadratic control problems with l 1 -control cost, Optim. Control Appl. Meth, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01286438

K. Alton and I. Mitchell, An Ordered Upwind Method with Precomputed Stencil and Monotone Node Acceptance for Solving Static Convex Hamilton-Jacobi Equations, Journal of Scientific Computing, vol.74, issue.250, pp.313-348, 2012.
DOI : 10.1007/s10915-011-9512-4

M. Bardi and I. Capuzzo-dolcetta, Optimal Control and Viscosity Solutions of Hamilton- Jacobi-Bellman Equations, 2008.
DOI : 10.1007/978-0-8176-4755-1

O. Bokanowski, S. Maroso, and H. Zidani, Some Convergence Results for Howard's Algorithm, SIAM Journal on Numerical Analysis, vol.47, issue.4, pp.3001-3026, 2009.
DOI : 10.1137/08073041X

N. Botkin, K. H. Hoffmann, and V. Turova, Stable Numerical Schemes for Solving Hamilton???Jacobi???Bellman???Isaacs Equations, SIAM Journal on Scientific Computing, vol.33, issue.2, pp.992-1007, 2011.
DOI : 10.1137/100801068

S. Cacace, E. Cristiani, M. Falcone, and A. Picarelli, A Patchy Dynamic Programming Scheme for a Class of Hamilton--Jacobi--Bellman Equations, SIAM Journal on Scientific Computing, vol.34, issue.5, pp.2625-2649, 2012.
DOI : 10.1137/110841576
URL : https://hal.archives-ouvertes.fr/inria-00628108

E. Carlini, M. Falcone, and R. Ferretti, An efficient algorithm for Hamilton???Jacobi equations in high dimension, Computing and Visualization in Science, vol.97, issue.1, pp.15-29, 2004.
DOI : 10.1007/s00791-004-0124-5

A. Chambolle and T. Pock, A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011.
DOI : 10.1007/s10851-010-0251-1
URL : https://hal.archives-ouvertes.fr/hal-00490826

E. Cristiani and M. Falcone, Fast Semi-Lagrangian Schemes for the Eikonal Equation and Applications, SIAM Journal on Numerical Analysis, vol.45, issue.5, pp.1979-2011, 2007.
DOI : 10.1137/050637625

M. Falcone, A numerical approach to the infinite horizon problem of deterministic control theory, Numerical methods for differential games based on partial differential equations, pp.1-13, 1987.

M. Falcone and R. Ferretti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations, 2014.
DOI : 10.1137/1.9781611973051
URL : https://hal.archives-ouvertes.fr/hal-00916055

H. Ishii, Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations, Indiana Univ, Math. J, vol.33, issue.5, pp.721-748, 1984.

K. Ito and K. Kunisch, Lagrange multiplier approach to variational problems and applications, 2008.
DOI : 10.1137/1.9780898718614

M. Jarczyk, Lokale Optimierungsstrategien in der dynamischen Programmierung, Diploma thesis, 2005.

A. Kröner, K. Kunisch, and H. Zidani, Optimal feedback control for undamped wave equations by solving a HJB equation, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.2, 2014.
DOI : 10.1051/cocv/2014033

H. Maurer and G. Vossen, On L 1 -minimization in optimal control and applications to robotics, Optim. Control Appl. Meth, vol.27, pp.301-321, 2006.

R. T. Rockafellar, Convex analysis, Convex Analysis, 1997.

J. Sethian and A. Vladimirsky, Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms, SIAM Journal on Numerical Analysis, vol.41, issue.1, pp.325-363, 2003.
DOI : 10.1137/S0036142901392742

M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces, 2011.
DOI : 10.1137/1.9781611970692

C. Unrath, Nichtglatte Optimierungsstrategien in der dynamischen Programmierung, Diploma thesis, 2006.

T. Valkonen, A primal-dual hybrid gradient method for non-linear operators with applications to MRI, Inverse Probl, vol.30, issue.5, 2014.

T. Xiong, M. Zhang, Y. Zhang, and C. Shu, Fast Sweeping Fifth Order WENO Scheme for Static Hamilton-Jacobi Equations with Accurate Boundary Treatment, Journal of Scientific Computing, vol.74, issue.1-3, pp.514-536, 2010.
DOI : 10.1007/s10915-010-9345-6