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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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

• 11B. Heymann.
  
  Mathematical contributions for the optimization and regulation of electricity production, Université Paris Saclay, September 2016.
  
  https://hal.archives-ouvertes.fr/tel-01416404

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, n^o 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, n^o 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, n^o 3.
  
  https://hal.archives-ouvertes.fr/hal-01120450

International Conferences with Proceedings

• 20B. Heymann, J. Frédéric Bonnans, F. Silva, G. Jimenez.
  
  A Stochastic Continuous Time Model for Microgrid Energy Management, in: ECC2016, Aalborg, Denmark, June 2016.
  
  https://hal.archives-ouvertes.fr/hal-01314078

Scientific Books (or Scientific Book chapters)

• 21F. Bonnans, S. Gaubert.
  
  Recherche opérationnelle. Aspects mathématiques et applications, Ellipse, March 2016, 391 p.
  
  https://hal.inria.fr/hal-01422645

Internal Reports

• 22M. S. Aronna, J. F. Bonnans, A. Kröner.
  
  Optimal control of PDEs in a complex space setting; application to the Schrödinger equation, Inria, 2016.
  
  https://hal.archives-ouvertes.fr/hal-01311421
• 23A. Philpott, F. Wahid, F. Bonnans.
  
  MIDAS: A Mixed Integer Dynamic Approximation Scheme, Inria Saclay Ile de France, June 2016, 22 p.
  
  https://hal.inria.fr/hal-01401950

Other Publications

• 24B. Heymann, A. Jofré.
  
  Mechanism design and allocation algorithms for network markets with piece-wise linear costs and externalities, December 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01416411
• 25B. Heymann, A. Jofré.
  
  Mechanism Design and Auctions for Electricity Network, May 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01315844
• 26B. Heymann, P. Martinon, F. Bonnans.
  
  Long term aging : an adaptative weights dynamic programming algorithm, July 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01349932
• 27P. Martinon, P. Picard, A. Raj.
  
  On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard, July 2016, working paper or preprint.
  
  https://hal-polytechnique.archives-ouvertes.fr/hal-01348551

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, n^o 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, n^o 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, n^o 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, n^o 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.
  
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• 39M. Crandall, P. Lions.
  
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• 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, n^o 2, pp. 95–116.
• 42W. Hager.
  
  Runge-Kutta methods in optimal control and the transformed adjoint system, in: Numerische Mathematik, 2000, vol. 87, n^o 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, n^o 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.