IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v86y2023i4d10.1007_s10898-023-01301-z.html
   My bibliography  Save this article

Second-order characterization of convex mappings in Banach spaces and its applications

Author

Listed:
  • Mohammad Taghi Nadi

    (University of Isfahan)

  • Jafar Zafarani

    (Sheikhbahaee University and University of Isfahan)

Abstract

We show that the positive semi-definiteness of the regular or limiting (Mordukhovich) second-order subdifferential of an approximately convex function is a sufficient condition for its convexity. As a consequence of our result, we obtain a second-order characterization for the class of lower- $$C^1$$ C 1 functions. Furthermore, we show by an example that positive semi-definiteness of the second-order subdifferential of convex functions is not a necessary condition for some cases. Also, a second-order characterization for C-convex mappings is obtained, and derive some applications in optimization.

Suggested Citation

  • Mohammad Taghi Nadi & Jafar Zafarani, 2023. "Second-order characterization of convex mappings in Banach spaces and its applications," Journal of Global Optimization, Springer, vol. 86(4), pages 1005-1023, August.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:4:d:10.1007_s10898-023-01301-z
    DOI: 10.1007/s10898-023-01301-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-023-01301-z
    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/s10898-023-01301-z?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. Mohammad Taghi Nadi & Jafar Zafarani, 2022. "Second-Order Optimality Conditions for Constrained Optimization Problems with $$C^1$$ C 1 Data Via Regular and Limiting Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 158-179, June.
    2. Ning E. & Wen Song & Yu Zhang, 2012. "Second order sufficient optimality conditions in vector optimization," Journal of Global Optimization, Springer, vol. 54(3), pages 537-549, November.
    3. Vsevolod Ivanov, 2013. "Characterizations of pseudoconvex functions and semistrictly quasiconvex ones," Journal of Global Optimization, Springer, vol. 57(3), pages 677-693, November.
    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. Bui Trong Kien & Trinh Duy Binh, 2023. "On the second-order optimality conditions for multi-objective optimal control problems with mixed pointwise constraints," Journal of Global Optimization, Springer, vol. 85(1), pages 155-183, January.
    2. Satoshi Suzuki & Daishi Kuroiwa, 2015. "Characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 62(3), pages 431-441, July.
    3. Zhenhua Peng & Yihong Xu, 2017. "New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 128-140, January.
    4. Vsevolod I. Ivanov, 2020. "Characterization of Radially Lower Semicontinuous Pseudoconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 368-383, February.
    5. 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.
    6. Yi-Hong Xu & Zhen-Hua Peng, 2018. "Second-Order M-Composed Tangent Derivative and Its Applications," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-20, October.
    7. Vsevolod I. Ivanov, 2019. "Characterizations of Solution Sets of Differentiable Quasiconvex Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 144-162, April.
    8. Satoshi Suzuki, 2019. "Optimality Conditions and Constraint Qualifications for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 963-976, December.
    9. Nguyen Thi Toan & Le Quang Thuy & Nguyen Tuyen & Yi-Bin Xiao, 2021. "Second-order KKT optimality conditions for multiobjective discrete optimal control problems," Journal of Global Optimization, Springer, vol. 79(1), pages 203-231, January.

    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:86:y:2023:i:4:d:10.1007_s10898-023-01301-z. 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.