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Bibliography

Major publications by the team in recent years
  • 1A. 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
  • 2M. S. Aronna, J. F. Bonnans, B. S. Goh.

    Second order analysis of state-constrained control-affine problems, in: Mathematical Programming, Series A, January 2016, vol. 160, no 1, pp. 115-147.

    https://hal.inria.fr/hal-01081111
  • 3M. S. Aronna, J. F. Bonnans, A. Kröner.

    Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations, in: Mathematical Programming B, November 2016, 32 p.

    https://hal.inria.fr/hal-01273496
  • 4M. 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 ]

    https://hal.inria.fr/inria-00631332
  • 5J. 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
  • 6J. 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 ]

    https://hal.inria.fr/inria-00634387
  • 7B. 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
  • 8L. Giraldi, P. Martinon, M. Zoppello.

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

    https://hal.archives-ouvertes.fr/hal-01098501
  • 9A. Kröner, K. Kunisch, B. Vexler.

    Semismooth Newton methods for optimal control of the wave equation with control constraints, in: SIAM Journal on Control and Optimization, 2011, vol. 49, no 2, pp. 830–858.

    http://dx.doi.org/10.1137/090766541
  • 10A. 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, vol. 21, no 2, pp. 442 - 464. [ DOI : 10.1051/cocv/2014033 ]

    https://hal.archives-ouvertes.fr/hal-00924089
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 12M. S. Aronna, J. F. Bonnans, B. S. Goh.

    Second order analysis of state-constrained control-affine problems, in: Mathematical Programming, Series A, January 2016, vol. 160, no 1, pp. 115-147.

    https://hal.inria.fr/hal-01081111
  • 13M. S. Aronna, J. F. Bonnans, A. Kröner.

    Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations, in: Mathematical Programming B, November 2016, 32 p.

    https://hal.inria.fr/hal-01273496
  • 14I. Ben Latifa, J. F. Bonnans, M. Mnif.

    Numerical methods for an optimal multiple stopping problem, in: Stochastics and Dynamics, January 2016, vol. 16, no 4, 27 p. [ DOI : 10.1142/S0219493716500167 ]

    https://hal.inria.fr/hal-01248282
  • 15F. J. Bonnans, J. Gianatti, F. J. Silva.

    On the convergence of the Sakawa-Shindo algorithm in stochastic control, in: Mathematical Control and Related Fields, September 2016. [ DOI : 10.3934/mcrf.2016008 ]

    https://hal-unilim.archives-ouvertes.fr/hal-01148272
  • 16J. Garcke, A. Kröner.

    Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids, in: Journal of Scientific Computing, 2016.

    https://hal.archives-ouvertes.fr/hal-01185912
  • 17C. Hermosilla.

    Legendre Transform and Applications to Finite and Infinite Optimization, in: Set-Valued and Variational Analysis, March 2016. [ DOI : 10.1007/s11228-016-0368-5 ]

    https://hal.inria.fr/hal-01055917
  • 18B. Heymann, J. F. Bonnans, P. Martinon, F. Silva, F. Lanas, G. Jimenez.

    Continuous Optimal Control Approaches to Microgrid Energy Management, in: Energy Systems, 2016.

    https://hal.inria.fr/hal-01129393
  • 19D. Kalise, A. Kröner, K. Kunisch.

    Local minimization algorithms for dynamic programming equations, in: SIAM Journal on Scientific Computing, 2016, vol. 38, no 3.

    https://hal.archives-ouvertes.fr/hal-01120450

International Conferences with Proceedings

Scientific Books (or Scientific Book chapters)

Internal Reports

Other Publications

References in notes
  • 28M. 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.
  • 29M. Bardi, I. Capuzzo-Dolcetta.

    Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems and Control: Foundations and Applications, Birkhäuser, Boston, 1997.
  • 30G. Barles.

    Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques et Applications, Springer, Paris, 1994, vol. 17.
  • 31G. 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.
  • 32G. Bliss.

    Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946.
  • 33J. 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.
  • 34J. 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.
  • 35J. 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.
  • 36J. 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.
  • 37J. 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.
  • 38A. E. Bryson, Y.-C. Ho.

    Applied optimal control, Hemisphere Publishing, New-York, 1975.
  • 39M. Crandall, P. Lions.

    Viscosity solutions of Hamilton Jacobi equations, in: Bull. American Mathematical Society, 1983, vol. 277, pp. 1–42.
  • 40A. 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.
  • 41J. 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.
  • 42W. Hager.

    Runge-Kutta methods in optimal control and the transformed adjoint system, in: Numerische Mathematik, 2000, vol. 87, no 2, pp. 247–282.
  • 43A. Ioffe, V. Tihomirov.

    Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian Edition: Nauka, Moscow, 1974.
  • 44N. 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.
  • 45J.-L. Lagrange.

    Mécanique analytique, Paris, 1788, reprinted by J. Gabay, 1989.
  • 46E. Lee, L. Markus.

    Foundations of optimal control theory, John Wiley, New York, 1967.
  • 47G. Leitmann.

    An introduction to optimal control, Mc Graw Hill, New York, 1966.
  • 48K. 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.
  • 49H. Pham.

    Optimisation et Contrôle Stochastique Appliqués à la Finance, Springer Verlag, 2007, no 61.
  • 50L. Pontryagin, V. Boltyanski, R. Gamkrelidze, E. Michtchenko.

    The Mathematical Theory of Optimal Processes, Wiley Interscience, New York, 1962.
  • 51L. Young.

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