IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v86y2017i3d10.1007_s00186-017-0596-y.html
   My bibliography  Save this article

On the Aubin property of a class of parameterized variational systems

Author

Listed:
  • H. Gfrerer

    (Johannes Kepler University Linz)

  • J. V. Outrata

    (Academy of Sciences of the Czech Republic
    Federation University of Australia)

Abstract

The paper deals with a new sharp condition ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class encompasses various types of parameterized variational inequalities/generalized equations with fairly general constraint sets. The new condition requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.

Suggested Citation

  • H. Gfrerer & J. V. Outrata, 2017. "On the Aubin property of a class of parameterized variational systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 443-467, December.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:3:d:10.1007_s00186-017-0596-y
    DOI: 10.1007/s00186-017-0596-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-017-0596-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-017-0596-y?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. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
    2. René Henrion & Alexander Y. Kruger & Jiří V. Outrata, 2013. "Some Remarks on Stability of Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 681-697, December.
    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. 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.
    2. A. Uderzo, 2014. "On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 47-78, July.
    3. Huynh Van Ngai & Nguyen Huu Tron & Michel Théra, 2014. "Metric Regularity of the Sum of Multifunctions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 355-390, February.
    4. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2017. "On the Stability and Solution Sensitivity of a Consumer Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 567-589, November.
    5. 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.
    6. Helmut Gfrerer & Jiří V. Outrata, 2016. "On Computation of Generalized Derivatives of the Normal-Cone Mapping and Their Applications," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1535-1556, November.
    7. Flåm, Sjur Didrik & Jongen, Hubertus Th. & Stein, Oliver, 2007. "Slopes of Shadow Prices and Lagrange Multipliers," Working Papers in Economics 05/07, University of Bergen, Department of Economics.
    8. Jin Zhang & Xide Zhu, 2022. "Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 564-597, February.
    9. M. H. Rashid & S. H. Yu & C. Li & S. Y. Wu, 2013. "Convergence Analysis of the Gauss–Newton-Type Method for Lipschitz-Like Mappings," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 216-233, July.
    10. C. H. Jeffrey Pang, 2011. "Generalized Differentiation with Positively Homogeneous Maps: Applications in Set-Valued Analysis and Metric Regularity," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 377-397, August.
    11. Nooshin Movahedian, 2017. "Bounded Lagrange multiplier rules for general nonsmooth problems and application to mathematical programs with equilibrium constraints," Journal of Global Optimization, Springer, vol. 67(4), pages 829-850, April.
    12. Michaël Gaydu & Michel Geoffroy & Yvesner Marcelin, 2016. "Prederivatives of convex set-valued maps and applications to set optimization problems," Journal of Global Optimization, Springer, vol. 64(1), pages 141-158, January.
    13. N. Q. Huy & D. S. Kim & K. V. Ninh, 2012. "Stability of Implicit Multifunctions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 558-571, November.
    14. Adrian Petruşel & Gabriela Petruşel & Jen-Chih Yao, 2019. "Pseudo-contractivity and Metric Regularity in Fixed Point Theory," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 5-18, January.
    15. B. S. Mordukhovich & T. T. A. Nghia & R. T. Rockafellar, 2015. "Full Stability in Finite-Dimensional Optimization," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 226-252, February.
    16. Boris S. Mordukhovich, 2007. "Variational Analysis in Nonsmooth Optimization and Discrete Optimal Control," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 840-856, November.
    17. N. D. Yen, 1997. "Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 199-225, April.
    18. Matthieu Maréchal, 2018. "Metric Subregularity in Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 541-558, March.
    19. Roberto Andreani & Gabriel Haeser & Leonardo M. Mito & C. Héctor Ramírez & Thiago P. Silveira, 2022. "Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 42-78, October.
    20. Sona Kilianova & Daniel Sevcovic, 2013. "Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for Constrained Dynamic Stochastic Optimal Allocation Problem," Papers 1307.3672, arXiv.org, revised Jul 2013.

    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:86:y:2017:i:3:d:10.1007_s00186-017-0596-y. 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.