Free Access
Volume 18, Number 3, July-September 2012
Page(s) 836 - 855
Published online 17 August 2011
  1. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems and Control : Foundations and Applications, Birkhäuser, Boston (1997). [Google Scholar]
  2. G. Barles, Solutions de viscosity des equations de Hamilton-Jacobi (Viscosity solutions of Hamilton-Jacobi equations), Mathematiques & Applications (Paris) 17. Springer-Verlag, Paris (1994). [Google Scholar]
  3. G. Barles and E.R. Jakobsen, On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. ESAIM : M2AN 36 (2002) 33–54. [CrossRef] [EDP Sciences] [Google Scholar]
  4. E.N. Barron and H. Ishii, The bellman equation for minimizing the maximum cost. Nonlinear Anal. 13 (1989) 1067–1090. [CrossRef] [MathSciNet] [Google Scholar]
  5. E.N. Barron and R. Jensen, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Commun. Partial Differ. Equ. 15 (1990) 1713–1742. [Google Scholar]
  6. A.G. Bhatt and V.S. Borkar, Occupation measures for controlled markov processes : Characterization and optimality. Ann. Probab. 24 (1996) 1531–1562. [CrossRef] [MathSciNet] [Google Scholar]
  7. V. Borkar and V. Gaitsgory, Averaging of singularly perturbed controlled stochastic differential equations. Appl. Math. Optim. 56 (2007) 169–209. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Buckdahn, D. Goreac and M. Quincampoix, Stochastic optimal control and linear programming approach. Appl. Math. Optim. 63 (2011) 257–276. [CrossRef] [MathSciNet] [Google Scholar]
  9. W.H. Fleming and D. Vermes, Convex duality approach to the optimal control of diffusions. SIAM J. Control Optim. 27 (1989) 1136–1155. [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31 (1993) 257–272. [CrossRef] [MathSciNet] [Google Scholar]
  11. V. Gaitsgory and M. Quincampoix, Linear programming approach to deterministic infinite horizon optimal control problems with discounting. SIAM J. Control Optim. 48 (2009) 2480–2512. [CrossRef] [MathSciNet] [Google Scholar]
  12. V. Gaitsgory and S. Rossomakhine, Linear programming approach to deterministic long run average problems of optimal control. SIAM J. Control Optim. 44 (2006) 2006–2037. [CrossRef] [MathSciNet] [Google Scholar]
  13. D. Goreac and O.S. Serea, Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems. Nonlinear Anal. 73 (2010) 2699–2713. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Goreac and O.S. Serea, Mayer and optimal stopping stochastic control problems with discontinuous cost. J. Math. Anal. Appl. 380 (2011) 327–342. [CrossRef] [MathSciNet] [Google Scholar]
  15. N.V. Krylov, On the rate of convergence of finte-difference approximations for bellman’s equations with variable coefficients. Probab. Theory Relat. Fields 117 (2000) 1–16. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Plaskacz and M. Quincampoix, Value-functions for differential games and control systems with discontinuous terminal cost. SIAM J. Control Optim. 39 (2001) 1485–1498. [CrossRef] [Google Scholar]
  17. M. Quincampoix and O.S. Serea, The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures. Nonlinear Anal. 72 (2010) 2803–2815. [CrossRef] [MathSciNet] [Google Scholar]
  18. O.S. Serea, Discontinuous differential games and control systems with supremum cost. J. Math. Anal. Appl. 270 (2002) 519–542. [CrossRef] [MathSciNet] [Google Scholar]
  19. O.S. Serea, On reflecting boundary problem for optimal control. SIAM J. Control Optim. 42 (2003) 559–575. [CrossRef] [MathSciNet] [Google Scholar]
  20. A.I. Subbotin, Generalized solutions of first-order PDEs, The dynamical optimization perspective. Birkhäuser, Basel (1994). [Google Scholar]
  21. C. Villani, Optimal Transport : Old and New. Springer (2009). [Google Scholar]
  22. R. Vinter, Convex duality and nonlinear optimal control. SIAM J. Control Optim. 31 (1993) 518–538. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.