IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v146y2010i2d10.1007_s10957-010-9649-6.html
   My bibliography  Save this article

Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach

Author

Listed:
  • E. Cristiani

    (Università di Salerno
    IAC-CNR)

  • P. Martinon

    (INRIA and CMAP École Polytechnique)

Abstract

The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered.

Suggested Citation

  • E. Cristiani & P. Martinon, 2010. "Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 321-346, August.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9649-6
    DOI: 10.1007/s10957-010-9649-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9649-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9649-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. F. Bonnans & P. Martinon & E. Trélat, 2008. "Singular Arcs in the Generalized Goddard’s Problem," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 439-461, November.
    2. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    3. M. Falcone, 2006. "Numerical Methods For Differential Games Based On Partial Differential Equations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 231-272.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yue Hu & Carri W. Chan & Jing Dong, 2022. "Optimal Scheduling of Proactive Service with Customer Deterioration and Improvement," Management Science, INFORMS, vol. 68(4), pages 2533-2578, April.
    2. Cacace, Simone & Oliviero, Alessio, 2024. "Reliable optimal controls for SEIR models in epidemiology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 523-542.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaoyue Li & John M. Mulvey, 2023. "Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network," Papers 2306.08809, arXiv.org.
    2. Mahmoud Mahfouz & Angelos Filos & Cyrine Chtourou & Joshua Lockhart & Samuel Assefa & Manuela Veloso & Danilo Mandic & Tucker Balch, 2019. "On the Importance of Opponent Modeling in Auction Markets," Papers 1911.12816, arXiv.org.
    3. Boute, Robert N. & Gijsbrechts, Joren & van Jaarsveld, Willem & Vanvuchelen, Nathalie, 2022. "Deep reinforcement learning for inventory control: A roadmap," European Journal of Operational Research, Elsevier, vol. 298(2), pages 401-412.
    4. M. Soledad Aronna & J. Frédéric Bonnans & Pierre Martinon, 2013. "A Shooting Algorithm for Optimal Control Problems with Singular Arcs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 419-459, August.
    5. Dawei Chen & Fangxu Mo & Ye Chen & Jun Zhang & Xinyu You, 2022. "Optimization of Ramp Locations along Freeways: A Dynamic Programming Approach," Sustainability, MDPI, vol. 14(15), pages 1-13, August.
    6. Alexander Moll & Meir Pachter & Eloy Garcia & David Casbeer & Dejan Milutinović, 2020. "Robust Policies for a Multiple-Pursuer Single-Evader Differential Game," Dynamic Games and Applications, Springer, vol. 10(1), pages 202-221, March.
    7. Contreras, Mauricio & Pellicer, Rely & Villena, Marcelo, 2017. "Dynamic optimization and its relation to classical and quantum constrained systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 12-25.
    8. Harrold, Daniel J.B. & Cao, Jun & Fan, Zhong, 2022. "Data-driven battery operation for energy arbitrage using rainbow deep reinforcement learning," Energy, Elsevier, vol. 238(PC).
    9. T. D. Pol & S. Gabbert & H.-P. Weikard & E. C. Ierland & E. M. T. Hendrix, 2017. "A Minimax Regret Analysis of Flood Risk Management Strategies Under Climate Change Uncertainty and Emerging Information," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(4), pages 1087-1109, December.
    10. Vanvuchelen, Nathalie & De Boeck, Kim & Boute, Robert N., 2024. "Cluster-based lateral transshipments for the Zambian health supply chain," European Journal of Operational Research, Elsevier, vol. 313(1), pages 373-386.
    11. Bartłomiej Kocot & Paweł Czarnul & Jerzy Proficz, 2023. "Energy-Aware Scheduling for High-Performance Computing Systems: A Survey," Energies, MDPI, vol. 16(2), pages 1-28, January.
    12. Wadi Khalid Anuar & Lai Soon Lee & Hsin-Vonn Seow & Stefan Pickl, 2021. "A Multi-Depot Vehicle Routing Problem with Stochastic Road Capacity and Reduced Two-Stage Stochastic Integer Linear Programming Models for Rollout Algorithm," Mathematics, MDPI, vol. 9(13), pages 1-44, July.
    13. Wojdyła, Tomasz & Kimmel, Marek & Bobrowski, Adam, 2011. "Time to the MRCA of a sample in a Wright–Fisher model with variable population size," Theoretical Population Biology, Elsevier, vol. 80(4), pages 265-271.
    14. Peter Schober & Julian Valentin & Dirk Pflüger, 2022. "Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 185-224, January.
    15. Adriano Festa & Richard B. Vinter, 2016. "Decomposition of Differential Games with Multiple Targets," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 848-875, June.
    16. Matthias Breuer & David Windisch, 2019. "Investment Dynamics and Earnings‐Return Properties: A Structural Approach," Journal of Accounting Research, Wiley Blackwell, vol. 57(3), pages 639-674, June.
    17. E. Trélat, 2012. "Optimal Control and Applications to Aerospace: Some Results and Challenges," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 713-758, September.
    18. Diefenbach, Heiko & Emde, Simon & Glock, Christoph H., 2020. "Loading tow trains ergonomically for just-in-time part supply," European Journal of Operational Research, Elsevier, vol. 284(1), pages 325-344.
    19. Michael J. Pennock & William B. Rouse & Diane L. Kollar, 2007. "Transforming the Acquisition Enterprise: A Framework for Analysis and a Case Study of Ship Acquisition," Systems Engineering, John Wiley & Sons, vol. 10(2), pages 99-117, June.
    20. Quetschlich, Mathias & Moetz, André & Otto, Boris, 2021. "Optimisation model for multi-item multi-echelon supply chains with nested multi-level products," European Journal of Operational Research, Elsevier, vol. 290(1), pages 144-158.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9649-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.