IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v85y2023i1d10.1007_s10898-022-01197-1.html
   My bibliography  Save this article

Second order analysis for robust inclusion systems and applications

Author

Listed:
  • V. D. Thinh

    (University of Science
    Vietnam National University
    Dong Thap University)

  • T. D. Chuong

    (Saigon University)

  • N. L. H. Anh

    (University of Science
    Vietnam National University)

Abstract

In this paper, we study an uncertain inequality system, where the input data are uncertain and belong to prescribed uncertainty sets. Using the deterministic approach in robust optimization, we treat this uncertain system by examining the so-called robust system. This approach enables us to compute the second order tangent sets for the solution set of the robust system and then obtain the second order epi-subderivative for the indicator function of its solution set. In this way, we are able to calculate the graphical derivative for the normal cone mapping of solution set of the robust system under certain qualification conditions. As applications, we establish second order necessary and sufficient optimality conditions, and derive necessary and sufficient conditions for stability properties such as the isolated calmness of optimization problems involving uncertain constraints under weak qualification conditions.

Suggested Citation

  • V. D. Thinh & T. D. Chuong & N. L. H. Anh, 2023. "Second order analysis for robust inclusion systems and applications," Journal of Global Optimization, Springer, vol. 85(1), pages 81-110, January.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:1:d:10.1007_s10898-022-01197-1
    DOI: 10.1007/s10898-022-01197-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01197-1
    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/s10898-022-01197-1?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. 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. 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.
    3. Thai Doan Chuong & Do Sang Kim, 2016. "Hölder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 596-611, May.
    4. N. D. Yen, 1995. "Lipschitz Continuity of Solutions of Variational Inequalities with a Parametric Polyhedral Constraint," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 695-708, 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. Thinh, Vo Duc & Chuong, Thai Doan & Le Hoang Anh, Nguyen, 2023. "Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications," Applied Mathematics and Computation, Elsevier, vol. 455(C).

    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. Vo Duc Thinh & Xiaolong Qin & Jen-Chih Yao, 2024. "Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2784-2817, December.
    2. 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.
    3. Wang, Jian & He, Xiaozheng & Peeta, Srinivas & Wang, Wei, 2022. "Globally convergent line search algorithm with Euler-based step size-determination method for continuous network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 119-144.
    4. M. A. Noor, 1997. "Sensitivity Analysis for Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 399-407, November.
    5. 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.
    6. Thai Doan Chuong & Do Sang Kim, 2018. "Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications," Annals of Operations Research, Springer, vol. 267(1), pages 81-99, August.
    7. Jafari, Ehsan & Boyles, Stephen D., 2016. "Improved bush-based methods for network contraction," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 298-313.
    8. D. Aussel & J. Cotrina, 2013. "Stability of Quasimonotone Variational Inequality Under Sign-Continuity," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 653-667, September.
    9. Daniela Osorio-González & José Guadalupe Flores-Muñiz & Nataliya Kalashnykova & Viacheslav Kalashnikov, 2024. "Consistent Conjectural Variations Equilibrium for a Bilevel Human Migration Model," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2354-2369, December.
    10. Lucian Coroianu, 2016. "Best Lipschitz Constants of Solutions of Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 853-875, September.
    11. Lu, Shu & (Marco) Nie, Yu, 2010. "Stability of user-equilibrium route flow solutions for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 609-617, May.
    12. P. Q. Khanh & L. M. Luu, 2007. "Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 329-339, June.
    13. 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.
    14. Le Tuan & Gue Lee & Pham Sach, 2010. "Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones," Journal of Global Optimization, Springer, vol. 47(4), pages 639-660, August.
    15. Michael Patriksson & R. Tyrrell Rockafellar, 2002. "A Mathematical Model and Descent Algorithm for Bilevel Traffic Management," Transportation Science, INFORMS, vol. 36(3), pages 271-291, August.
    16. Tong, Jun & Hu, Jiaqiao & Hu, Jianqiang, 2017. "Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints," European Journal of Operational Research, Elsevier, vol. 256(1), pages 24-34.
    17. X. P. Ding & C. L. Luo, 1999. "On Parametric Generalized Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 195-205, January.
    18. Ashkan Mohammadi & Boris S. Mordukhovich, 2022. "Optimality Conditions for Variational Problems in Incomplete Functional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 139-157, June.
    19. 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.
    20. Thai Doan Chuong, 2019. "Stability of Implicit Multifunctions via Point-Based Criteria and Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 920-943, December.

    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:85:y:2023:i:1:d:10.1007_s10898-022-01197-1. 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.