IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v58y2014i3p595-612.html
   My bibliography  Save this article

Mordukhovich subgradients of the value function to a parametric discrete optimal control problem

Author

Listed:
  • N. Toan
  • J.-C. Yao

Abstract

This paper is devoted to the study of the first-order behavior of the value function of a parametric discrete optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Mordukhovich subdifferential of the value function of a parametric mathematical programming problem, we derive a formula for computing the Mordukhovich subdifferential of the value function to a parametric discrete optimal control problem. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • N. Toan & J.-C. Yao, 2014. "Mordukhovich subgradients of the value function to a parametric discrete optimal control problem," Journal of Global Optimization, Springer, vol. 58(3), pages 595-612, March.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:3:p:595-612
    DOI: 10.1007/s10898-013-0062-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0062-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-013-0062-1?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. Boris S. Mordukhovich & Nguyen Mau Nam, 2005. "Variational Stability and Marginal Functions via Generalized Differentiation," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 800-816, November.
    2. Alberto Seeger, 1996. "Subgradients of Optimal-Value Functions in Dynamic Programming: The Case of Convex Systems Without Optimal Paths," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 555-575, August.
    3. Kien, B.T. & Liou, Y.C. & Wong, N.-C. & Yao, J.-C., 2009. "Subgradients of value functions in parametric dynamic programming," European Journal of Operational Research, Elsevier, vol. 193(1), pages 12-22, February.
    4. Zhaotong Lian & Liming Liu & Marcel F. Neuts, 2005. "A Discrete-Time Model for Common Lifetime Inventory Systems," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 718-732, August.
    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. N. T. Toan & Q. H. Ansari & J.-C. Yao, 2015. "Second-Order Necessary Optimality Conditions for a Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 812-836, June.
    2. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.
    3. Le Quang Thuy & Nguyen Thi Toan, 2016. "Subgradients of the Value Function in a Parametric Convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 43-64, July.
    4. Le Quang Thuy & Bui Thi Thanh & Nguyen Thi Toan, 2017. "On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 421-442, May.

    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. Le Quang Thuy & Nguyen Thi Toan, 2016. "Subgradients of the Value Function in a Parametric Convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 43-64, July.
    2. Kien, B.T. & Liou, Y.C. & Wong, N.-C. & Yao, J.-C., 2009. "Subgradients of value functions in parametric dynamic programming," European Journal of Operational Research, Elsevier, vol. 193(1), pages 12-22, February.
    3. N. H. Chieu & B. T. Kien & N. T. Toan, 2016. "Further Results on Subgradients of the Value Function to a Parametric Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 785-801, March.
    4. Kanzi, N. & Nobakhtian, S., 2010. "Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems," European Journal of Operational Research, Elsevier, vol. 205(2), pages 253-261, September.
    5. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.
    6. Boris S. Mordukhovich & Nguyen Mau Nam & Hung M. Phan, 2012. "Variational Analysis of Marginal Functions with Applications to Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 557-586, March.
    7. Huanan Zhang & Cong Shi & Xiuli Chao, 2016. "Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs," Operations Research, INFORMS, vol. 64(2), pages 432-440, April.
    8. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    9. Opher Baron & Oded Berman & David Perry, 2010. "Continuous review inventory models for perishable items ordered in batches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 217-247, October.
    10. Le Quang Thuy & Bui Thi Thanh & Nguyen Thi Toan, 2017. "On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 421-442, May.
    11. N. T. Toan & Q. H. Ansari & J.-C. Yao, 2015. "Second-Order Necessary Optimality Conditions for a Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 812-836, June.
    12. Pahl, Julia & Voß, Stefan, 2014. "Integrating deterioration and lifetime constraints in production and supply chain planning: A survey," European Journal of Operational Research, Elsevier, vol. 238(3), pages 654-674.
    13. Khanh, Phan Quoc & Quyen, Ho Thuc & Yao, Jen-Chih, 2011. "Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials," European Journal of Operational Research, Elsevier, vol. 212(2), pages 235-241, July.
    14. A. Krishnamoorthy & Dhanya Shajin & B. Lakshmy, 2016. "On a queueing-inventory with reservation, cancellation, common life time and retrial," Annals of Operations Research, Springer, vol. 247(1), pages 365-389, December.
    15. Bhawna Kohli, 2012. "Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 632-651, March.
    16. Stephan Dempe & Alain B. Zemkoho, 2011. "The Generalized Mangasarian-Fromowitz Constraint Qualification and Optimality Conditions for Bilevel Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 46-68, January.
    17. S. Dempe & A. Zemkoho, 2012. "Bilevel road pricing: theoretical analysis and optimality conditions," Annals of Operations Research, Springer, vol. 196(1), pages 223-240, July.
    18. Duong Thi Viet An & Jen-Chih Yao, 2019. "Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 126-143, April.
    19. N. Toan & L. Thuy, 2016. "Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints," Journal of Global Optimization, Springer, vol. 64(3), pages 533-562, March.
    20. Onno Boxma & David Perry & Wolfgang Stadje & Shelley Zacks, 2022. "A compound Poisson EOQ model for perishable items with intermittent high and low demand periods," Annals of Operations Research, Springer, vol. 317(2), pages 439-459, October.

    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:jglopt:v:58:y:2014:i:3:p:595-612. 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.