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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

Articles in International Peer-Reviewed Journals

  • 10A. Aftalion, J. F. Bonnans.

    Optimization of running strategies based on anaerobic energy and variations of velocity, in: SIAM Journal of Applied Mathematics, October 2014, vol. 74, no 5, pp. 1615-1636.

    https://hal.inria.fr/hal-00851182
  • 11K. Barty, J. F. Bonnans, L. Pfeiffer.

    Sensitivity analysis for the outages of nuclear power plants, in: Energy Systems, June 2014, vol. 5, no 2, pp. 371-406. [ DOI : 10.1007/s12667-013-0096-y ]

    https://hal.inria.fr/hal-00671186
  • 12T. Bayen, J. F. Bonnans, F. J. Silva.

    Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations, in: Transactions American Mathematical Society, April 2014, vol. 366, no 4, pp. 2063–2087. [ DOI : 10.1090/S0002-9947-2013-05961-2 ]

    https://hal.inria.fr/inria-00632308
  • 13T. 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, June 2014, 24 p. [ DOI : 10.1002/oca.2127 ]

    https://hal.archives-ouvertes.fr/hal-00860570
  • 14O. Bokanowski, A. Picarelli, H. Zidani.

    Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost, in: Applied Mathematics and Optimization, 2014. [ DOI : 10.1007/s00245-014-9255-3 ]

    https://hal.inria.fr/hal-00931025
  • 15J. F. Bonnans.

    Optimal control of a semilinear parabolic equation with singular arcs, in: Optimization, Methods and Software, September 2014, vol. 29, no 2, pp. 964-978. [ DOI : 10.1080/10556788.2013.830220 ]

    https://hal.inria.fr/hal-00740698
  • 16J. F. Bonnans, X. Dupuis, L. Pfeiffer.

    Second-order necessary conditions in Pontryagin form for optimal control problems, in: SIAM Journal on Control and Optimization, 2014, vol. 52, no 6, pp. 3887-3916. [ DOI : 10.1137/130923452 ]

    https://hal.inria.fr/hal-00825273
  • 17J. F. Bonnans, X. Dupuis, L. Pfeiffer.

    Second-order sufficient conditions for strong solutions to optimal control problems, in: ESAIM: Control, Optimisation and Calculus of Variations, March 2014, vol. 20, no 03, pp. 704-724. [ DOI : 10.1051/cocv/2013080 ]

    https://hal.inria.fr/hal-00825260
  • 18B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, in: Acta Applicandae Mathematicae, June 2014, 43 p. [ DOI : 10.1007/s10440-014-9947-3 ]

    https://hal.inria.fr/hal-00867753
  • 19X. Dupuis.

    Optimal control of leukemic cell population dynamics, in: Mathematical Modeling for Natural Phenomena, 2014, vol. 9, no 1, pp. 4-26. [ DOI : 10.1051/mmnp/20149102 ]

    https://hal.inria.fr/hal-00858208
  • 20R. Ferretti, H. Zidani.

    Monotone numerical schemes and feedback construction for hybrid control systems, in: Journal of Optimization Theory and Applications, 2014. [ DOI : 10.1007/s10957-014-0637-0 ]

    https://hal.inria.fr/hal-00989492
  • 21G. Granato, H. Zidani.

    Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints, in: SIAM Journal on Control and Optimization, 2014, vol. 52, no 1, pp. 606–628. [ DOI : 10.1137/120874205 ]

    https://hal.inria.fr/hal-00735724
  • 22L. Grüne, H. Zidani.

    Zubov's equation for state-constrained perturbed nonlinear systems, in: Mathematical Control and Related Fields, 2014.

    https://hal.inria.fr/hal-00931028
  • 23C. 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
  • 24A. Kröner, K. Kunisch.

    A minimum effort optimal control problem for the wave equation, in: Computational Optimization and Applications, January 2014, vol. 57, no 1, pp. 241-270.

    https://hal.archives-ouvertes.fr/hal-01089336
  • 25A. Kröner, K. Kunisch, H. Zidani.

    Optimal feedback control of undamped wave equations by solving a HJB equation, in: ESAIM: Control, Optimisation and Calculus of Variations, 2014, pp. 1–25.

    https://hal.archives-ouvertes.fr/hal-00924089
  • 26R. Muñoz-Tamayo, P. Martinon, G. Bougaran, F. Mairet, O. Bernard.

    Getting the most out of it: optimal experiments for parameter estimation of microalgae growth models, in: Journal of Process Control, May 2014, pp. 991-1001. [ DOI : 10.1016/j.jprocont.2014.04.021 ]

    https://hal.inria.fr/hal-00998525
  • 27Z. Rao, A. Siconolfi, H. Zidani.

    Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations, in: Journal of Differential Equations, 2014, vol. 257, no 11, pp. 3978–4014. [ DOI : 10.1016/j.jde.2014.07.015 ]

    https://hal.inria.fr/hal-00820273

Invited Conferences

  • 28A. Kröner, D. Kalise, M. Falcone.

    A semi-Lagrangian scheme for Lp-penalized minimum time problems, in: 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, Netherlands, July 2014, pp. 1798-1803.

    https://hal.archives-ouvertes.fr/hal-01089877

International Conferences with Proceedings

  • 29A. Kröner, D. Kalise.

    Reduced-order minimum time control of advection-reaction-diffusion systems via dynamic programming, in: 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, France, July 2014, pp. 1196-1202.

    https://hal.archives-ouvertes.fr/hal-01089887

Internal Reports

  • 30J. F. Bonnans, A. Festa.

    Error estimates for the Euler discretization of an optimal control problem with first-order state constraints, Inria Saclay, December 2014.

    https://hal.inria.fr/hal-01093229

Patents

  • 31G. Granato, J. F. Bonnans, K. Aouchiche, R. Grégory, H. Zidani.

    Energy management method for an electric vehicle, November 2014, no US Patent 20,140,350,763 2014.

    https://hal.inria.fr/hal-01090084

Other Publications

References in notes
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    High order numerical discretization for Hamilton-Jacobi equations on triangular meshes, in: J. Scientific Computing, 2000, vol. 15, no 2, pp. 197–229.
  • 46M. 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.
  • 47J. Aubin, H. Frankowska.

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  • 52J. 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.
  • 53J. 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.
  • 54J. 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.
  • 55F. J. Bonnans, P. Martinon, V. Grélard.

    Bocop - A collection of examples, Inria, 2012, no RR-8053.

    http://hal.inria.fr/hal-00726992
  • 56J. 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.
  • 57J. 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.
  • 58B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance, 2013.

    https://hal.inria.fr/hal-00867753
  • 59A. E. Bryson, Y.-C. Ho.

    Applied optimal control, Hemisphere Publishing, New-York, 1975.
  • 60F. Clarke.

    A new approach to Lagrange multipliers, in: Mathematics of Operations Research, 1976, vol. 2, pp. 165-174.
  • 61M. 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.
  • 62M. Crandall, P. Lions.

    Viscosity solutions of Hamilton Jacobi equations, in: Bull. American Mathematical Society, 1983, vol. 277, pp. 1–42.
  • 63M. Crandall, P. Lions.

    Two approximations of solutions of Hamilton-Jacobi equations, in: Mathematics of Computation, 1984, vol. 43, pp. 1–19.
  • 64B. Després, F. Lagoutière.

    Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, in: J. Sci. Comput., 2001, vol. 16, pp. 479-524.
  • 65B. 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.
  • 66A. 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.
  • 67I. Ekeland.

    Nonconvex minimization problems, in: Bulletin of the American Mathematical Society, 1979, vol. 1(New series), pp. 443-474.
  • 68M. 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.
  • 69M. 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.
  • 70J. 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.
  • 71L. Giraldi, P. Martinon, M. Zoppello.

    Controllability and Optimal Strokes for N-link Micro-swimmer, 2013.

    https://hal.archives-ouvertes.fr/hal-00798363
  • 72L. Giraldi, P. Martinon, M. Zoppello.

    Optimal Design for Purcell Three-link Swimmer, September 2014.

    https://hal.archives-ouvertes.fr/hal-01098501
  • 73W. Hager.

    Runge-Kutta methods in optimal control and the transformed adjoint system, in: Numerische Mathematik, 2000, vol. 87, no 2, pp. 247–282.
  • 74E. Harten.

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  • 76A. Ioffe, V. Tihomirov.

    Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian Edition: Nauka, Moscow, 1974.
  • 77N. 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.
  • 78A. Kröner, D. Kalise, M. Falcone.

    A semi-Lagrangian scheme for Lp-penalized minimum time problems, in: 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, Netherlands, July 2014, pp. 1798-1803.

    https://hal.archives-ouvertes.fr/hal-01089877
  • 79A. Kröner, D. Kalise.

    Reduced-order minimum time control of advection-reaction-diffusion systems via dynamic programming. , in: 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, France, July 2014, pp. 1196-1202.

    https://hal.archives-ouvertes.fr/hal-01089887
  • 80A. Kröner, K. Kunisch.

    A minimum effort optimal control problem for the wave equation., in: Computational Optimization and Applications, January 2014, vol. 57, no 1, pp. 241-270.

    https://hal.archives-ouvertes.fr/hal-01089336
  • 81A. Kröner, S. S. Rodrigues.

    Internal exponential stabilization to a nonstationary solution for 1D Burgers equations with piecewise constant controls, December 2014.

    https://hal.archives-ouvertes.fr/hal-01089896
  • 82A. Kröner, S. S. Rodrigues.

    Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations, December 2014.

    https://hal.archives-ouvertes.fr/hal-01089893
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    Hamilton-Jacobi-Bellman Equations on Multi-Domains, in: Control and Optimization with PDE Constraints, K. Bredies, C. Clason, K. Kunisch, G. von Winckel (editors), International Series of Numerical Mathematics, Springer, May 2013, vol. 164, pp. 93–116. [ DOI : 10.1007/978-3-0348-0631-2_6 ]

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