IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v147y2018icp121-139.html
   My bibliography  Save this article

Domain decomposition based parallel Howard’s algorithm

Author

Listed:
  • Festa, Adriano

Abstract

The Howard’s algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A useful characteristic of the method is the superlinear convergence which, in presence of a finite number of controls, is reached in finite time. Performances of the method can be significantly improved using parallel computing. Building a parallel version of the method is not trivial because of the hyperbolic nature of the problem. In this paper we propose a parallel version of the Howard’s algorithm driven by an idea of domain decomposition. This permits to derive some important properties and to prove the convergence under standard assumptions. The good features of the algorithm are shown through some tests and examples.

Suggested Citation

  • Festa, Adriano, 2018. "Domain decomposition based parallel Howard’s algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 121-139.
    • Handle: RePEc:eee:matcom:v:147:y:2018:i:c:p:121-139
    DOI: 10.1016/j.matcom.2017.04.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475417301684
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2017.04.008?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. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    2. Manuel Santos & John Rust, "undated". "Convergence Properties of Policy Iteration," Working Papers 2133377, Department of Economics, W. P. Carey School of Business, Arizona State University.
    3. Martin L. Puterman & Shelby L. Brumelle, 1979. "On the Convergence of Policy Iteration in Stationary Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 60-69, February.
    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. Roberto Ferretti & Adriano Festa, 2019. "Optimal Route Planning for Sailing Boats: A Hybrid Formulation," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1015-1032, June.

    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. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.
    2. Ozak, Omer, 2014. "Optimal consumption under uncertainty, liquidity constraints, and bounded rationality," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 237-254.
    3. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    4. Ayşe Kabukçuoğlu & Enrique Martínez-García, 2021. "A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 435-460, August.
    5. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    6. Ayse Kabukcuoglu & Enrique Martínez-García, 2016. "The Market Resources Method for Solving Dynamic Optimization Problems," Koç University-TUSIAD Economic Research Forum Working Papers 1607, Koc University-TUSIAD Economic Research Forum.
    7. Elisabetta Carlini & Adriano Festa & Francisco J. Silva & Marie-Therese Wolfram, 2017. "A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow," Dynamic Games and Applications, Springer, vol. 7(4), pages 683-705, December.
    8. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    9. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    10. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    11. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    12. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    13. Andrew Ching & Susumu Imai & Masakazu Ishihara & Neelam Jain, 2012. "A practitioner’s guide to Bayesian estimation of discrete choice dynamic programming models," Quantitative Marketing and Economics (QME), Springer, vol. 10(2), pages 151-196, June.
    14. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    15. Changming Ji & Chuangang Li & Boquan Wang & Minghao Liu & Liping Wang, 2017. "Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4571-4586, November.
    16. Ghassan, Hassan B. & Al-Jefri, Essam H., 2015. "الحساب الجاري في المدى البعيد عبر نموذج داخلي الزمن [The Current Account in the Long Run through the Intertemporal Model]," MPRA Paper 66527, University Library of Munich, Germany.
    17. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    18. Ohno, Katsuhisa & Boh, Toshitaka & Nakade, Koichi & Tamura, Takayoshi, 2016. "New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system," European Journal of Operational Research, Elsevier, vol. 249(1), pages 22-31.
    19. Oleg Malafeyev & Achal Awasthi, 2015. "A Dynamic Model of Functioning of a Bank," Papers 1511.01529, arXiv.org.
    20. Bellemare, Charles, 2007. "A life-cycle model of outmigration and economic assimilation of immigrants in Germany," European Economic Review, Elsevier, vol. 51(3), pages 553-576, April.

    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:eee:matcom:v:147:y:2018:i:c:p:121-139. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.