IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3376-d1208826.html
   My bibliography  Save this article

Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems

Author

Listed:
  • Meiju Luo

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

  • Menghan Du

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

  • Yue Zhang

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

Abstract

In this paper, we consider stochastic mixed vector variational inequality problems. Firstly, we present an equivalent form for the stochastic mixed vector variational inequality problems. Secondly, we present a deterministic bi-criteria model for giving the reasonable resolution of the stochastic mixed vector variational inequality problems and further propose the approximation problem for solving the given deterministic model by employing the smoothing technique and the sample average approximation method. Thirdly, we obtain the convergence analysis for the proposed approximation problem while the sample space is compact. Finally, we propose a compact approximation method when the sample space is not a compact set and provide the corresponding convergence results.

Suggested Citation

  • Meiju Luo & Menghan Du & Yue Zhang, 2023. "Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems," Mathematics, MDPI, vol. 11(15), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3376-:d:1208826
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3376/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/15/3376/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Smith, Adam, 1977. "An Inquiry into the Nature and Causes of the Wealth of Nations," University of Chicago Press Economics Books, University of Chicago Press, number 9780226763743 edited by Cannan, Edwin, October.
    2. M. J. Luo & G. H. Lin, 2009. "Expected Residual Minimization Method for Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 103-116, January.
    3. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, October.
    4. M. J. Luo & G. H. Lin, 2009. "Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 569-581, September.
    Full references (including those not matched with items on IDEAS)

    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. Fang Lu & Shengjie Li & Jing Yang, 2015. "Convergence analysis of weighted expected residual method for nonlinear stochastic variational inequality problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 229-242, October.
    2. Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.
    3. Lu, Fang & Li, Sheng-jie, 2015. "Method of weighted expected residual for solving stochastic variational inequality problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 651-663.
    4. Carbonnier Cl´ement, 2014. "The incidence of non-linear consumption taxes," Научный результат. Серия «Экономические исследования», CyberLeninka;Федеральное государственное автономное образовательное учреждение высшего образования «Белгородский государственный национальный исследовательский университет», issue 1, pages 5-18.
    5. Yichen Lu & Chao Yang & Jun Yang, 2022. "A multi-objective humanitarian pickup and delivery vehicle routing problem with drones," Annals of Operations Research, Springer, vol. 319(1), pages 291-353, December.
    6. Wu, Weitiao & Lin, Yue & Liu, Ronghui & Jin, Wenzhou, 2022. "The multi-depot electric vehicle scheduling problem with power grid characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 322-347.
    7. Bogdana Stanojević & Milan Stanojević & Sorin Nădăban, 2021. "Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    8. Stelios Rozakis & Athanasios Kampas, 2022. "An interactive multi-criteria approach to admit new members in international environmental agreements," Operational Research, Springer, vol. 22(4), pages 3461-3487, September.
    9. Manuel V. C. Vieira & Margarida Carvalho, 2023. "Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer," 4OR, Springer, vol. 21(3), pages 491-512, September.
    10. Petr Iakovlevitch Ekel & Matheus Pereira Libório & Laura Cozzi Ribeiro & Mateus Alberto Dorna de Oliveira Ferreira & Joel Gomes Pereira Junior, 2024. "Multi-Criteria Decision under Uncertainty as Applied to Resource Allocation and Its Computing Implementation," Mathematics, MDPI, vol. 12(6), pages 1-20, March.
    11. Klaus Jaffé, 2015. "Visualizing the Invisible Hand of Markets: Simulating Complex Dynamic Economic Interactions," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 22(2), pages 115-132, April.
    12. Yeudiel Lara Moreno & Carlos Ignacio Hernández Castellanos, 2024. "A Hierarchical Approach to a Tri-Objective Portfolio Optimization Problem Considering an ESG Index," Mathematics, MDPI, vol. 12(19), pages 1-16, October.
    13. Bennet Gebken & Sebastian Peitz, 2021. "Inverse multiobjective optimization: Inferring decision criteria from data," Journal of Global Optimization, Springer, vol. 80(1), pages 3-29, May.
    14. Fernando García-Castaño & Miguel Ángel Melguizo-Padial & G. Parzanese, 2023. "Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 367-382, June.
    15. Gabriel Felbermayr, 2023. "Krieg mit anderen Mitteln," WIFO Monatsberichte (monthly reports), WIFO, vol. 96(2), pages 111-122, February.
    16. Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    17. Christopher J. Coyne & Rachel L. Mathers, 2011. "Introduction," Chapters, in: Christopher J. Coyne & Rachel L. Mathers (ed.), The Handbook on the Political Economy of War, chapter 1, Edward Elgar Publishing.
    18. Brian Whitaker & Lindsey Godwin, 2013. "The Antecedents of Moral Imagination in the Workplace: A Social Cognitive Theory Perspective," Journal of Business Ethics, Springer, vol. 114(1), pages 61-73, April.
    19. Stefano Bosi & Claire Rogel Gaillard, 2018. "Biologie prédictive pour la santé. Regards croisés sur les enjeux socio-économiques et scientifiques chez l'Homme, les animaux et les plantes," Post-Print hal-02786221, HAL.
    20. Uhlig, Harald, 2012. "Economics and reality," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 29-41.

    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:gam:jmathe:v:11:y:2023:i:15:p:3376-:d:1208826. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.