IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v57y2013i4p1375-1384.html
   My bibliography  Save this article

Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities

Author

Listed:
  • Songnian He
  • Hong-Kun Xu

Abstract

A uniqueness theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Three examples are given to demonstrate the usefulness and advantages of our alternative theorem. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Songnian He & Hong-Kun Xu, 2013. "Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1375-1384, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1375-1384
    DOI: 10.1007/s10898-012-9995-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9995-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9995-z?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. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, 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. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2024. "Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems," Networks and Spatial Economics, Springer, vol. 24(2), pages 425-459, June.
    2. Anindya Bhattacharya & Francesco Ciardiello, 2022. "On spatial majority voting with an even (vis-a-vis odd) number of voters: a note," Papers 2208.06849, arXiv.org.
    3. Anindya Bhattacharya & Francesco Ciardiello, 2024. "How sensitive are the results in voting theory when just one other voter joins in? Some instances with spatial majority voting," Discussion Papers 24/03, Department of Economics, University of York.
    4. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.

    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. Joseph Y. J. Chow & Amelia C. Regan, 2011. "Real Option Pricing of Network Design Investments," Transportation Science, INFORMS, vol. 45(1), pages 50-63, February.
    2. Ferrari, Paolo, 2010. "Willingness to spend and road pricing rates," Transport Policy, Elsevier, vol. 17(3), pages 160-172, May.
    3. Du, Muqing & Tan, Heqing & Chen, Anthony, 2021. "A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models," European Journal of Operational Research, Elsevier, vol. 290(3), pages 982-999.
    4. Michael Patriksson & R. Tyrrell Rockafellar, 2003. "Sensitivity Analysis of Aggregated Variational Inequality Problems, with Application to Traffic Equilibria," Transportation Science, INFORMS, vol. 37(1), pages 56-68, February.
    5. Yang, Hai & Meng, Qiang, 1998. "Departure time, route choice and congestion toll in a queuing network with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 247-260, May.
    6. Chih-Peng Chu & Jyh-Fa Tsai, 2004. "Road Pricing models with maintenance cost," Transportation, Springer, vol. 31(4), pages 457-477, November.
    7. Yang, Hai & Huang, Hai-Jun, 1998. "Principle of marginal-cost pricing: how does it work in a general road network?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 45-54, January.
    8. Romilly, Peter, 2004. "Welfare evaluation with a road capacity constraint," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(4), pages 287-303, May.
    9. Fournier, Nicholas, 2021. "Hybrid pedestrian and transit priority zoning policies in an urban street network: Evaluating network traffic flow impacts with analytical approximation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 152(C), pages 254-274.
    10. Yang, Hai & Meng, Qiang, 2000. "Highway pricing and capacity choice in a road network under a build-operate-transfer scheme," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(3), pages 207-222, April.
    11. Poulopoulou, Maria & Spyropoulou, Ioanna, 2019. "Active traffic management in urban areas: Is it effective for professional drivers? The case of variable message signs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 130(C), pages 412-423.
    12. Chen, Xiaoming & Zhou, Xuesong & List, George F., 2011. "Using time-varying tolls to optimize truck arrivals at ports," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 965-982.
    13. Ding, Hongxing & Yang, Hai & Xu, Hongli & Li, Ting, 2023. "Status quo-dependent user equilibrium model with adaptive value of time," Transportation Research Part B: Methodological, Elsevier, vol. 170(C), pages 77-90.
    14. Yildirim, Mehmet Bayram & Hearn, Donald W., 2005. "A first best toll pricing framework for variable demand traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 659-678, September.
    15. Yang, Hai & Bell, Michael G. H. & Meng, Qiang, 2000. "Modeling the capacity and level of service of urban transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 255-275, May.
    16. Yang, Hai & Wang, Xiaolei, 2011. "Managing network mobility with tradable credits," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 580-594, March.
    17. Loukas Dimitriou & Theodore Tsekeris & Antony Stathopoulos, 2009. "Joint pricing and design of urban highways with spatial and user group heterogeneity," Netnomics, Springer, vol. 10(1), pages 141-160, April.
    18. Yang, Hai & Meng, Qiang & Lee, Der-Horng, 2004. "Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 477-493, July.
    19. Yang, Hai & Tang, Wilson H. & Man Cheung, Wing & Meng, Qiang, 2002. "Profitability and welfare gain of private toll roads in a network with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(6), pages 537-554, July.
    20. Tu, Ningwen & Li, Zhi-Chun & Fu, Xiaowen & Lei, Zheng, 2020. "Airline network competition in inter-continental market," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).

    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:57:y:2013:i:4:p:1375-1384. 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.