IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v265y2018i2p448-453.html
   My bibliography  Save this article

Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping

Author

Listed:
  • Wu, Zili

Abstract

For a variational inequality problem with a pseudomonotone mapping F, we characterize the weak sharpness of its solution set C* without using gap functions. When the mapping F is also constant on C*, the characterizations of weak sharpness of C* become more succinct. As an example, a pseudomonotone+ mapping on C* is shown to be constant on C*. Consequently the weak sharpness of C* can further be described by a Gâteaux differentiable function which itself characterizes the pseudomonotonicity+ of F on C*. It turns out that several existing relevant results with differentiable gap functions can be obtained from ours.

Suggested Citation

  • Wu, Zili, 2018. "Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping," European Journal of Operational Research, Elsevier, vol. 265(2), pages 448-453.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:2:p:448-453
    DOI: 10.1016/j.ejor.2017.09.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717308809
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.09.037?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. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
    2. Wu, Zili & Wu, Soon-Yi, 2008. "Gateaux differentiability of the dual gap function of a variational inequality," European Journal of Operational Research, Elsevier, vol. 190(2), pages 328-344, October.
    3. Laengle, Sigifredo & Merigó, José M. & Miranda, Jaime & Słowiński, Roman & Bomze, Immanuel & Borgonovo, Emanuele & Dyson, Robert G. & Oliveira, José Fernando & Teunter, Ruud, 2017. "Forty years of the European Journal of Operational Research: A bibliometric overview," European Journal of Operational Research, Elsevier, vol. 262(3), pages 803-816.
    4. Li, J. & Huang, N.J. & Yang, X.Q., 2010. "Weak sharp minima for set-valued vector variational inequalities with an application," European Journal of Operational Research, Elsevier, vol. 205(2), pages 262-272, September.
    5. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    6. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    7. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    8. Jiang, Jian-Lin & Yuan, Xiao-Ming, 2008. "A heuristic algorithm for constrained multi-source Weber problem - The variational inequality approach," European Journal of Operational Research, Elsevier, vol. 187(2), pages 357-370, June.
    9. Li, Min & Yuan, Xiao-Ming, 2008. "An APPA-based descent method with optimal step-sizes for monotone variational inequalities," European Journal of Operational Research, Elsevier, vol. 186(2), pages 486-495, April.
    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. Shipra Singh & Savin Treanţă, 2021. "Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis," Annals of Operations Research, Springer, vol. 302(1), pages 265-287, July.
    2. Ruyu Wang & Wenling Zhao & Daojin Song & Yaozhong Hu, 2024. "The Augmented Weak Sharpness of Solution Sets in Equilibrium Problems," Mathematics, MDPI, vol. 12(2), pages 1-23, January.
    3. Luong Nguyen & Qamrul Hasan Ansari & Xiaolong Qin, 2020. "Linear conditioning, weak sharpness and finite convergence for equilibrium problems," Journal of Global Optimization, Springer, vol. 77(2), pages 405-424, 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. Seyit Kerimkhulle & Nataliia Obrosova & Alexander Shananin & Akylbek Tokhmetov, 2023. "Young Duality for Variational Inequalities and Nonparametric Method of Demand Analysis in Input–Output Models with Inputs Substitution: Application for Kazakhstan Economy," Mathematics, MDPI, vol. 11(19), pages 1-22, October.
    2. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    3. Shipra Singh & Savin Treanţă, 2021. "Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis," Annals of Operations Research, Springer, vol. 302(1), pages 265-287, July.
    4. Bing-sheng He & Wei Xu & Hai Yang & Xiao-Ming Yuan, 2011. "Solving Over-production and Supply-guarantee Problems in Economic Equilibria," Networks and Spatial Economics, Springer, vol. 11(1), pages 127-138, March.
    5. Younes Hamdouch & Qiang Patrick Qiang & Kilani Ghoudi, 2017. "A Closed-Loop Supply Chain Equilibrium Model with Random and Price-Sensitive Demand and Return," Networks and Spatial Economics, Springer, vol. 17(2), pages 459-503, June.
    6. Yunda Dong, 2021. "Weak convergence of an extended splitting method for monotone inclusions," Journal of Global Optimization, Springer, vol. 79(1), pages 257-277, January.
    7. Gaviria-Marin, Magaly & Merigó, José M. & Baier-Fuentes, Hugo, 2019. "Knowledge management: A global examination based on bibliometric analysis," Technological Forecasting and Social Change, Elsevier, vol. 140(C), pages 194-220.
    8. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    9. Xiaomei Dong & Xingju Cai & Deren Han & Zhili Ge, 2020. "Solving a Class of Variational Inequality Problems with a New Inexact Strategy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-20, January.
    10. Guido Gentile, 2018. "New Formulations of the Stochastic User Equilibrium with Logit Route Choice as an Extension of the Deterministic Model," Service Science, INFORMS, vol. 52(6), pages 1531-1547, December.
    11. Anna Nagurney & Qiang Qiang, 2008. "An efficiency measure for dynamic networks modeled as evolutionary variational inequalities with application to the Internet and vulnerability analysis," Netnomics, Springer, vol. 9(1), pages 1-20, January.
    12. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
    13. Ahipaşaoğlu, Selin Damla & Meskarian, Rudabeh & Magnanti, Thomas L. & Natarajan, Karthik, 2015. "Beyond normality: A cross moment-stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 333-354.
    14. Satish Kumar & Filomena Maggino & Raj V. Mahto & Riya Sureka & Leonardo Salvatore Alaimo & Weng Marc Lim, 2022. "Social Indicators Research: A Retrospective Using Bibliometric Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 162(1), pages 413-448, July.
    15. Ran, Bin & Hall, Randolph & Boyce, David E., 1995. "A Link-Based Variational Inequality Model for Dynamic Departure Time/Route Choice," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt84t190b3, Institute of Transportation Studies, UC Berkeley.
    16. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    17. Younes Hamdouch & Siriphong Lawphongpanich, 2010. "Congestion Pricing for Schedule-Based Transit Networks," Transportation Science, INFORMS, vol. 44(3), pages 350-366, August.
    18. Hamdouch, Younes & Lawphongpanich, Siriphong, 2008. "Schedule-based transit assignment model with travel strategies and capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 663-684, August.
    19. Zhang, Ding & Nagurney, Anna & Wu, Jiahao, 2001. "On the equivalence between stationary link flow patterns and traffic network equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 731-748, September.
    20. Xiaoming Yuan, 2011. "An improved proximal alternating direction method for monotone variational inequalities with separable structure," Computational Optimization and Applications, Springer, vol. 49(1), pages 17-29, May.

    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:ejores:v:265:y:2018:i:2:p:448-453. 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.elsevier.com/locate/eor .

    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.