EN FR
EN FR


previous Previous | up Home


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.

    http://hal.inria.fr/inria-00193157
  • 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

  • 10X. Dupuis.

    Contrôle optimal d'équations différentielles avec - ou sans - mémoire, Ecole Polytechnique X, November 2013.

    http://hal.inria.fr/tel-00914246
  • 11L. Pfeiffer.

    Analyse de sensibilité pour des problèmes de commande optimale. Commande optimale stochastique sous contrainte en probabilité, Ecole Polytechnique X, November 2013.

    http://hal.inria.fr/pastel-00881119
  • 12Z. Rao.

    L'approche Hamilton-Jacobi-Bellman pour des problèmes de contrôle optimal avec des coefficients discontinus, Ecole Polytechnique X, December 2013.

    http://hal.inria.fr/pastel-00927358

Articles in International Peer-Reviewed Journals

  • 13A. Altarovici, O. Bokanowski, H. Zidani.

    A general Hamilton-Jacobi framework for nonlinear state-constrained control problems, in: ESAIM: Control, Optimisation and Calculus of Variations, 2013, vol. 19, no 2, pp. 337–357. [ DOI : 10.1051/cocv/2012011 ]

    http://hal.inria.fr/hal-00653337
  • 14M. S. Aronna, J. F. Bonnans, P. Martinon.

    A Shooting Algorithm for Optimal Control Problems with Singular Arcs, in: Journal of Optimization Theory and Applications, August 2013, vol. 158, no 2, pp. 419-459. [ DOI : 10.1007/s10957-012-0254-8 ]

    http://hal.inria.fr/inria-00631332
  • 15O. Bokanowski, Y. Cheng, C.-W. Shu.

    A discontinuous Galerkin scheme for front propagation with obstacles, in: Numerische Mathematik, June 2013. [ DOI : 10.1007/s00211-013-0555-3 ]

    http://hal.inria.fr/hal-00653532
  • 16J. F. Bonnans.

    Optimal control of a semilinear parabolic equation with singular arcs, in: Optimization, Methods and Software, August 2013, 14 p. [ DOI : 10.1080/10556788.2013.830220 ]

    http://hal.inria.fr/hal-00740698
  • 17J. F. Bonnans, C. De La Vega, X. Dupuis.

    First and second order optimality conditions for optimal control problems of state constrained integral equations, in: Journal of Optimization Theory and Applications, 2013, vol. 159, no 1, pp. 1-40. [ DOI : 10.1007/s10957-013-0299-3 ]

    http://hal.inria.fr/hal-00697504
  • 18J. F. Bonnans, L. Pfeiffer, O. S. Serea.

    Sensitivity analysis for relaxed optimal control problems with final-state constraints, in: Nonlinear Analysis: Theory, Methods & Applications, September 2013, vol. 89, pp. 55-80. [ DOI : 10.1016/j.na.2013.04.013 ]

    http://hal.inria.fr/hal-00702246
  • 19J. F. Bonnans, X. Tan.

    A model-free no-arbitrage price bound for variance options, in: Applied Mathematics and Optimization, July 2013, vol. 68, no 1, pp. 43-73. [ DOI : 10.1007/s00245-013-9197-1 ]

    http://hal.inria.fr/inria-00634387
  • 20N. Forcadel, Z. Rao, H. Zidani.

    State-constrained Optimal Control Problems of Impulsive Differential Equations, in: Applied Mathematics and Optimization, 2013. [ DOI : 10.1007/s00245-013-9193-5 ]

    http://hal.inria.fr/hal-00653671
  • 21G. Granato, H. Zidani.

    Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints, in: SIAM Journal on Control and Optimization, 2014.

    http://hal.inria.fr/hal-00735724
  • 22C. Imbert, R. Monneau, H. Zidani.

    A Hamilton-Jacobi approach to junction problems and application to traffic flows, in: ESAIM - Control Optimisation and Calculus of Variations, 2013, vol. 19, no 01, pp. 129-166, This paper is dedicated to J.-B. Hiriart-Urruty. Note on v3: to appear in ESAIM: COCV. [ DOI : 10.1051/cocv/2012002 ]

    http://hal.inria.fr/hal-00569010

International Conferences with Proceedings

  • 23J. F. Bonnans.

    Singular arcs in the optimal control of a parabolic equation, in: 13th European Control Conference, Zurich, Switzerland, July 2013.

    http://hal.inria.fr/hal-00845704
  • 24J. F. Bonnans.

    The shooting approach to optimal control problems, in: IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, Caen, France, F. Giri, V. van Assche (editors), IFAC, July 2013, pp. 281-292. [ DOI : 10.3182/20130703-3-FR-4038.00158 ]

    http://hal.inria.fr/hal-00830896
  • 25B. Bonnard, M. Claeys, O. Cots, P. Martinon.

    Comparison of Numerical Methods in the Contrast Imaging Problem in NMR, in: 52nd IEEE Conference on Decision and Control, Firenze, Italy, December 2013.

    http://hal.inria.fr/hal-00800436
  • 26A. Festa, R. Vinter.

    A decomposition technique for pursuit evasion games with many pursuers, in: 52nd IEEE Control and Decision Conference (CDC), Florence, Italy, 2013, 7 p.

    http://hal.inria.fr/hal-00916864
  • 27R. Muñoz-Tamayo, P. Martinon, G. Bougaran, F. Mairet, O. Bernard.

    Design of Optimal Experiments for Parameter Estimation of Microalgae Growth Models, in: Computer Applied to Biotechnology, Mumbai, India, December 2013.

    http://hal.inria.fr/hal-00856749

Scientific Books (or Scientific Book chapters)

  • 28Z. Rao, H. Zidani.

    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 ]

    http://hal.inria.fr/hal-00803108

Internal Reports

  • 29A. Aftalion, J. F. Bonnans.

    Optimization of running strategies based on anaerobic energy and variations of velocity, Inria, August 2013, no RR-8344, 22 p.

    http://hal.inria.fr/hal-00851182
  • 30T. Bayen, F. Mairet, P. Martinon, M. Sebbah.

    Optimizing the anaerobic digestion of microalgae in a coupled process, September 2013.

    http://hal.inria.fr/hal-00860570
  • 31J. F. Bonnans, X. Dupuis, L. Pfeiffer.

    Second-order necessary conditions in Pontryagin form for optimal control problems, Inria, May 2013, no RR-8306, 37 p.

    http://hal.inria.fr/hal-00825273
  • 32J. F. Bonnans, X. Dupuis, L. Pfeiffer.

    Second-order sufficient conditions for strong solutions to optimal control problems, Inria, May 2013, no RR-8307, 24 p.

    http://hal.inria.fr/hal-00825260
  • 33X. Dupuis.

    Optimal control of leukemic cell population dynamics, Inria, August 2013, no RR-8356, 25 p.

    http://hal.inria.fr/hal-00858208

Other Publications

References in notes
  • 44R. 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.
  • 45R. 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.
  • 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.

    Set-valued analysis, Birkhäuser, Boston, 1990.
  • 48M. Bardi, I. Capuzzo-Dolcetta.

    Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems and Control: Foundations and Applications, Birkhäuser, Boston, 1997.
  • 49G. Barles.

    Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques et Applications, Springer, Paris, 1994, vol. 17.
  • 50G. 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.
  • 51G. Bliss.

    Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946.
  • 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, August 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.
  • 58A. E. Bryson, Y.-C. Ho.

    Applied optimal control, Hemisphere Publishing, New-York, 1975.
  • 59F. Clarke.

    A new approach to Lagrange multipliers, in: Mathematics of Operations Research, 1976, vol. 2, pp. 165-174.
  • 60M. 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.
  • 61M. Crandall, P. Lions.

    Viscosity solutions of Hamilton Jacobi equations, in: Bull. American Mathematical Society, 1983, vol. 277, pp. 1–42.
  • 62M. Crandall, P. Lions.

    Two approximations of solutions of Hamilton-Jacobi equations, in: Mathematics of Computation, 1984, vol. 43, pp. 1–19.
  • 63B. Després, F. Lagoutière.

    Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, in: J. Sci. Comput., 2001, vol. 16, pp. 479-524.
  • 64B. 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.
  • 65A. 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.
  • 66I. Ekeland.

    Nonconvex minimization problems, in: Bulletin of the American Mathematical Society, 1979, vol. 1(New series), pp. 443-474.
  • 67M. 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.
  • 68M. 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.
  • 69J. 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.
  • 70W. Hager.

    Runge-Kutta methods in optimal control and the transformed adjoint system, in: Numerische Mathematik, 2000, vol. 87, no 2, pp. 247–282.
  • 71E. Harten.

    ENO schemes with subcell resolution, in: J. Computational Physics, 1989, vol. 83, pp. 148–184.
  • 72C. 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.
  • 73A. Ioffe, V. Tihomirov.

    Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian Edition: Nauka, Moscow, 1974.
  • 74J. B. Keller.

    A Theory of Competitive Running, in: Physics Today, 1973, vol. 26, no 9, pp. 42–47.
  • 75J. B. Keller.

    Optimal velocity in a race, in: Amer. Math. Monthly, 1974, vol. 81, pp. 474–480.
  • 76N. 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.
  • 77H. Kushner, P. Dupuis.

    Numerical methods for stochastic control problems in continuous time, Applications of mathematics, Springer, New York, 2001, vol. 24, Second edition.
  • 78J.-L. Lagrange.

    Mécanique analytique, Paris, 1788, reprinted by J. Gabay, 1989.
  • 79E. Lee, L. Markus.

    Foundations of optimal control theory, John Wiley, New York, 1967.
  • 80G. Leitmann.

    An introduction to optimal control, Mc Graw Hill, New York, 1966.
  • 81K. Malanowski, C. Büskens, H. Maurer.

    Convergence of approximations to nonlinear optimal control problems, in: Mathematical programming with data perturbations, New York, Lecture Notes in Pure and Appl. Math., Dekker, 1998, vol. 195, pp. 253–284.
  • 82S. Osher, C.-W. Shu.

    High essentially nonoscillatory schemes for Hamilton-Jacobi equations, in: SIAM J. Numer. Anal., 1991, vol. 28, no 4, pp. 907-922.
  • 83H. Pham.

    Optimisation et Contrôle Stochastique Appliqués à la Finance, Springer Verlag, 2007, no 61.
  • 84L. Pontryagin, V. Boltyanski, R. Gamkrelidze, E. Michtchenko.

    The Mathematical Theory of Optimal Processes, Wiley Interscience, New York, 1962.
  • 85P. Roe.

    Some contributions to the modelling of discontinuous flows, in: Lectures in Applied Mathematics, 1985, vol. 22, pp. 163–193.
  • 86L. Young.

    Lectures on the calculus of variations and optimal control theory, W. B. Saunders Co., Philadelphia, 1969.
  • 87B. Øksendal.

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


previous Previous | up Home