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Bibliography

Major publications by the team in recent years
  • 1O. Bokanowski, B. Bruder, S. Maroso, H. Zidani.

    Numerical approximation for a superreplication problem under gamma constraints, in: SIAM. Num. Analysis., 2009, vol. 47(3), pp. 2289–2320.
  • 2O. Bokanowski, N. Megdich, H. Zidani.

    Convergence of a non-monotone scheme for Hamilton-Jacobi-Bellman equations with discontinuous data, in: Numerische Mathematik / Numerical Mathematics, 2010, vol. 115, no 1, pp. 1–44.
  • 3J. F. Bonnans, J. C. Gilbert, C. Lemaréchal, C. Sagastizábal.

    Numerical Optimization: theoretical and numerical aspects, Universitext, Springer-Verlag, Berlin, 2006, second edition.
  • 4J. F. Bonnans, S. Maroso, H. Zidani.

    Error estimates for a stochastic impulse control problem, in: Appl. Math. and Optim., 2007, vol. 55, no 3, pp. 327–357.
  • 5J. F. Bonnans, A. Shapiro.

    Perturbation analysis of optimization problems, Springer-Verlag, New York, 2000.
  • 6J. F. Bonnans, H. Zidani.

    Consistency of generalized finite difference schemes for the stochastic HJB equation, in: SIAM J. Numerical Analysis, 2003, vol. 41, pp. 1008-1021.
  • 7N. Bérend, J. F. Bonnans, J. Laurent-Varin, M. Haddou, C. Talbot.

    An Interior-Point Approach to Trajectory Optimization, in: J. Guidance, Control and Dynamics, 2007, vol. 30, no 5, pp. 1228-1238.
  • 8J. Gergaud, P. Martinon.

    Using switching detection and variational equations for the shooting method, in: Optimal Control Applications and Methods, 2007, vol. 28, no 2, pp. 95–116.
  • 9P. Martinon, J. F. Bonnans, J. Laurent-Varin, E. Trélat.

    Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher, in: J. Guidance, Control, and Dynamics, 2009, vol. 32, no 1, pp. 51-55.
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 12T. Bayen, F. Mairet, P. Martinon, M. Sebbah.

    Analysis of a periodic optimal control problem connected to microalgae anaerobic digestion, in: Optimal Control Applications and Methods, November 2015, 24 p. [ DOI : 10.1002/oca.2127 ]

    https://hal.archives-ouvertes.fr/hal-00860570
  • 13I. Ben Latifa, J. F. Bonnans, M. Mnif.

    A General Optimal Multiple Stopping Problem with an Application to Swing Options, in: Stochastic Analysis and Applications, June 2015, vol. 33, 25 p. [ DOI : 10.1080/07362994.2015.1037592 ]

    https://hal.inria.fr/hal-01248283
  • 14I. Ben Latifa, J. F. Bonnans, M. Mnif.

    Numerical methods for an optimal multiple stopping problem, in: Stochastics and Dynamics, September 2015, vol. 16, no 4, 27 p. [ DOI : 10.1142/S0219493716500167 ]

    https://hal.inria.fr/hal-01248282
  • 15O. Bokanowski, A. Picarelli, H. Zidani.

    Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost, in: Applied Mathematics and Optimization, 2015, vol. 71, no 1, pp. 125–163. [ DOI : 10.1007/s00245-014-9255-3 ]

    https://hal.inria.fr/hal-00931025
  • 16B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, in: Acta Applicandae Mathematicae, February 2015, vol. 135, no 1, pp. 5-45. [ DOI : 10.1007/s10440-014-9947-3 ]

    https://hal.inria.fr/hal-00867753
  • 17P. Cardaliaguet, P. J. Graber.

    Mean field games systems of first order, in: ESAIM - Control Optimisation and Calculus of Variations, 2015, vol. 21, no 3, pp. 690–722.

    https://hal.archives-ouvertes.fr/hal-00925905
  • 18P. Cardaliaguet, J. Graber, A. Porretta, D. Tonon.

    Second order mean field games with degenerate diffusion and local coupling, in: NoDEA. Nonlinear Differential Equations and Applications, 2015, vol. 22, no 5, pp. 1287-1317.

    https://hal.archives-ouvertes.fr/hal-01049834
  • 19R. Ferretti, H. Zidani.

    Monotone numerical schemes and feedback construction for hybrid control systems, in: Journal of Optimization Theory and Applications, 2015, vol. 165, no 2, pp. 507-531. [ DOI : 10.1007/s10957-014-0637-0 ]

    https://hal.inria.fr/hal-00989492
  • 20L. Giraldi, P. Martinon, M. Zoppello.

    Optimal Design for Purcell Three-link Swimmer, in: Physical Review, February 2015, vol. 91, no 2, 023012.

    https://hal.archives-ouvertes.fr/hal-01098501
  • 21L. Grüne, H. Zidani.

    Zubov's equation for state-constrained perturbed nonlinear systems, in: Mathematical Control and Related Fields, 2015, vol. 5, no 1, pp. 55-71. [ DOI : 10.3934/mcrf.2015.5.55 ]

    https://hal.inria.fr/hal-00931028
  • 22C. Hermosilla, H. Zidani.

    Infinite horizon problems on stratifiable state-constraints sets, in: Journal of Differential Equations, February 2015, vol. 258, no 4, pp. 1430–1460. [ DOI : 10.1016/j.jde.2014.11.001 ]

    https://hal.inria.fr/hal-00955921
  • 23A. Kröner, S. S. Rodrigues.

    Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations, in: SIAM Journal on Control and Optimization, 2015, vol. 53, no 2, pp. 1020–1055.

    https://hal.archives-ouvertes.fr/hal-01089893

Conferences without Proceedings

  • 24A. Kröner, S. S. Rodrigues.

    Internal exponential stabilization to a nonstationary solution for 1D Burgers equations with piecewise constant controls, in: Control Conference (ECC), 2015 European, Linz, Austria, July 2015, pp. 2676-2681. [ DOI : 10.1109/ECC.2015.7330942 ]

    https://hal.archives-ouvertes.fr/hal-01089896

Internal Reports

Scientific Popularization

Other Publications

  • 31P. Bettiol, B. Bonnard, L. Giraldi, P. Martinon, J. Rouot.

    The Purcell Three-link swimmer: some geometric and numerical aspects related to periodic optimal controls, October 2015, working paper or preprint.

    https://hal.inria.fr/hal-01143763
  • 32F. J. Bonnans, J. Gianatti, F. J. Silva.

    On the convergence of the Sakawa-Shindo algorithm in stochastic control, December 2015, working paper or preprint.

    https://hal-unilim.archives-ouvertes.fr/hal-01148272
  • 33B. Heymann, J. F. Bonnans, P. Martinon, F. Silva, F. Lanas, G. Jimenez.

    Continuous Optimal Control Approaches to Microgrid Energy Management, March 2015, working paper or preprint.

    https://hal.inria.fr/hal-01129393
References in notes
  • 34R. Abgrall.

    Numerical discretization of boundary conditions for first order Hamilton-Jacobi equations, in: SIAM J. Numerical Analysis, 2003, vol. 41, no 6, pp. 2233–2261.
  • 35R. Abgrall, S. Augoula.

    High order numerical discretization for Hamilton-Jacobi equations on triangular meshes, in: J. Scientific Computing, 2000, vol. 15, no 2, pp. 197–229.
  • 36M. S. Aronna, J. F. Bonnans, P. Martinon.

    A Shooting Algorithm for Optimal Control Problems with Singular Arcs, in: Journal of Optimization Theory and Applications, 2013, Inria Report RR-7763, 2011.
  • 37J. Aubin, H. Frankowska.

    Set-valued analysis, Birkhäuser, Boston, 1990.
  • 38M. Bardi, I. Capuzzo-Dolcetta.

    Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems and Control: Foundations and Applications, Birkhäuser, Boston, 1997.
  • 39G. Barles.

    Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques et Applications, Springer, Paris, 1994, vol. 17.
  • 40G. Barles, E. Jakobsen.

    Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations, in: SIAM J. Numerical Analysis, 2005, vol. 43, no 2, pp. 540–558.
  • 41G. Bliss.

    Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946.
  • 42J. F. Bonnans, A. Hermant.

    Well-Posedness of the Shooting Algorithm for State Constrained Optimal Control Problems with a Single Constraint and Control, in: SIAM J. Control Optimization, 2007, vol. 46, no 4, pp. 1398–1430.
  • 43J. F. Bonnans, A. Hermant.

    Second-order Analysis for Optimal Control Problems with Pure State Constraints and Mixed Control-State Constraints, in: Annales de l'Institut Henri Poincaré. Analyse non linéaire, 2009, vol. 26, no 2, pp. 561-598.
  • 44J. F. Bonnans, J. Laurent-Varin.

    Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control, in: Numerische Mathematik, 2006, vol. 103, no 1, pp. 1–10.
  • 45J. F. Bonnans, E. Ottenwaelter, H. Zidani.

    Numerical schemes for the two dimensional second-order HJB equation, in: ESAIM: M2AN, 2004, vol. 38, pp. 723-735.
  • 46J. F. Bonnans, H. Zidani.

    Consistency of generalized finite difference schemes for the stochastic HJB equation, in: SIAM J. Numerical Analysis, 2003, vol. 41, pp. 1008-1021.
  • 47A. E. Bryson, Y.-C. Ho.

    Applied optimal control, Hemisphere Publishing, New-York, 1975.
  • 48F. Clarke.

    A new approach to Lagrange multipliers, in: Mathematics of Operations Research, 1976, vol. 2, pp. 165-174.
  • 49M. Crandall, L. Evans, P. Lions.

    Some properties of viscosity solutions of Hamilton-Jacobi equations, in: Trans. Amer. Math. Soc, 1984, vol. 282, pp. 487-502.
  • 50M. Crandall, P. Lions.

    Viscosity solutions of Hamilton Jacobi equations, in: Bull. American Mathematical Society, 1983, vol. 277, pp. 1–42.
  • 51M. Crandall, P. Lions.

    Two approximations of solutions of Hamilton-Jacobi equations, in: Mathematics of Computation, 1984, vol. 43, pp. 1–19.
  • 52B. Després, F. Lagoutière.

    Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, in: J. Sci. Comput., 2001, vol. 16, pp. 479-524.
  • 53B. Després, F. Lagoutière.

    A non-linear anti-diffusive scheme for the linear advection equation, in: C. R. Acad. Sci. Paris, Série I, Analyse numérique, 1999, vol. 328, pp. 939-944.
  • 54A. Dontchev, W. Hager, V. Veliov.

    Second-order Runge-Kutta approximations in control constrained optimal control, in: SIAM Journal on Numerical Analysis, 2000, vol. 38, pp. 202–226.
  • 55I. Ekeland.

    Nonconvex minimization problems, in: Bulletin of the American Mathematical Society, 1979, vol. 1(New series), pp. 443-474.
  • 56M. Falcone, R. Ferretti.

    Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods, in: Journal of Computational Physics, 2002, vol. 175, pp. 559–575.
  • 57M. Falcone, R. Ferretti.

    Convergence analysis for a class of high-order semi-Lagrangian advection schemes, in: SIAM J. Numer. Anal., 1998, vol. 35, no 3, pp. 909–940.
  • 58J. Gergaud, P. Martinon.

    Using switching detection and variational equations for the shooting method, in: Optimal Control Applications and Methods, 2007, vol. 28, no 2, pp. 95–116.
  • 59W. Hager.

    Runge-Kutta methods in optimal control and the transformed adjoint system, in: Numerische Mathematik, 2000, vol. 87, no 2, pp. 247–282.
  • 60E. Harten.

    ENO schemes with subcell resolution, in: J. Computational Physics, 1989, vol. 83, pp. 148–184.
  • 61C. Hu, C.-W. Shu.

    A discontinuous Galerkin finite element method for Hamilton-Jacobi equations, in: SIAM J. on Scientific Computing, 1999, vol. 21, no 2, pp. 666–690.
  • 62A. Ioffe, V. Tihomirov.

    Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian Edition: Nauka, Moscow, 1974.
  • 63N. Krylov.

    On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients, in: Probability Theory and Related Fields, 2000, vol. 117, pp. 1–16.
  • 64H. Kushner, P. Dupuis.

    Numerical methods for stochastic control problems in continuous time, Applications of mathematics, Springer, New York, 2001, vol. 24, Second edition.
  • 65J.-L. Lagrange.

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  • 66E. Lee, L. Markus.

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  • 67G. Leitmann.

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  • 68K. Malanowski, C. Büskens, H. Maurer.

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  • 69S. Osher, C.-W. Shu.

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  • 70H. Pham.

    Optimisation et Contrôle Stochastique Appliqués à la Finance, Springer Verlag, 2007, no 61.
  • 71L. Pontryagin, V. Boltyanski, R. Gamkrelidze, E. Michtchenko.

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  • 72P. Roe.

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  • 73L. Young.

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  • 74B. Øksendal.

    Stochastic differential equations, Universitext, Sixth, Springer-Verlag, Berlin, 2003.


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