IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v78y2013i2p243-258.html
   My bibliography  Save this article

Variational inequalities over Euclidean balls

Author

Listed:
  • Nguyen Qui

Abstract

This paper investigates solution stability of parametric variational inequalities over Euclidean balls in finite dimensional spaces. We provide exact formulas for computing required coderivatives of the normal cone mappings to Euclidean balls via the initial data. On the basis of these formulas, we establish necessary and sufficient conditions for Lipschitzian stability of the solution maps of the aforementioned variational inequalities. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Nguyen Qui, 2013. "Variational inequalities over Euclidean balls," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 243-258, October.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:2:p:243-258
    DOI: 10.1007/s00186-013-0442-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-013-0442-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-013-0442-9?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. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2011. "Properties of two DC algorithms in quadratic programming," Journal of Global Optimization, Springer, vol. 49(3), pages 481-495, March.
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    3. Shu Lu & Stephen M. Robinson, 2008. "Variational Inequalities over Perturbed Polyhedral Convex Sets," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 689-711, August.
    4. J.-C. Yao & N. D. Yen, 2010. "Parametric Variational System with a Smooth-Boundary Constraint Set," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 205-221, Springer.
    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. Nguyen Thanh Qui, 2014. "Generalized Differentiation of a Class of Normal Cone Operators," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 398-429, May.
    2. Nguyen Thanh Qui, 2016. "Coderivatives of implicit multifunctions and stability of variational systems," Journal of Global Optimization, Springer, vol. 65(3), pages 615-635, July.

    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. Nguyen Qui, 2014. "Stability for trust-region methods via generalized differentiation," Journal of Global Optimization, Springer, vol. 59(1), pages 139-164, May.
    2. Nguyen Thanh Qui, 2012. "Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 98-122, April.
    3. Alan Beggs, 2018. "Sensitivity analysis of boundary equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 763-786, October.
    4. Shu Lu, 2008. "Sensitivity of Static Traffic User Equilibria with Perturbations in Arc Cost Function and Travel Demand," Transportation Science, INFORMS, vol. 42(1), pages 105-123, February.
    5. Nguyen Thanh Qui, 2016. "Coderivatives of implicit multifunctions and stability of variational systems," Journal of Global Optimization, Springer, vol. 65(3), pages 615-635, July.
    6. Duong Thi Kim Huyen & Jen-Chih Yao & Nguyen Dong Yen, 2019. "Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 91-116, January.
    7. M. Durea & R. Strugariu, 2011. "On parametric vector optimization via metric regularity of constraint systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 409-425, December.
    8. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    9. Liang Chen & Anping Liao, 2020. "On the Convergence Properties of a Second-Order Augmented Lagrangian Method for Nonlinear Programming Problems with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 248-265, October.
    10. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    11. Francisco Aragón Artacho & Boris Mordukhovich, 2011. "Enhanced metric regularity and Lipschitzian properties of variational systems," Journal of Global Optimization, Springer, vol. 50(1), pages 145-167, May.
    12. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    13. Guo, Qiangqiang & Ban, Xuegang (Jeff), 2023. "A multi-scale control framework for urban traffic control with connected and automated vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 175(C).
    14. J. Han & D. Sun, 1997. "Newton and Quasi-Newton Methods for Normal Maps with Polyhedral Sets," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 659-676, September.
    15. 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.
    16. U. Felgenhauer, 1999. "Regularity Properties of Optimal Controls with Application to Discrete Approximation," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 97-110, July.
    17. Ilker Birbil, S. & Gürkan, G. & Listes, O.L., 2004. "Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints : Sample-Path Analysis," Discussion Paper 2004-25, Tilburg University, Center for Economic Research.
    18. Yong-Jin Liu & Li Wang, 2016. "Properties associated with the epigraph of the $$l_1$$ l 1 norm function of projection onto the nonnegative orthant," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 205-221, August.
    19. A. F. Izmailov & M. V. Solodov, 2015. "Newton-Type Methods: A Broader View," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 577-620, February.
    20. J. V. Outrata, 1999. "Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 627-644, August.

    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:mathme:v:78:y:2013:i:2:p:243-258. 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.