IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v77y2020i3d10.1007_s10898-020-00889-w.html
   My bibliography  Save this article

Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds

Author

Listed:
  • M. Farrokhiniya

    (Lorestan University)

  • A. Barani

    (Lorestan University)

Abstract

We provide definitions for Fréchet $$\varepsilon $$ε-subdifferential and Fréchet $$\varepsilon $$ε-normals set for functions and sets in the Riemannian manifolds. Then we generalize the notions of Mordukhovich sequential subdifferential and normal cone (limiting subdifferential and normal cone) and develop several calculus rules for subdifferentials and normal cones in this setting. Finally, as an application, the limiting subdifferential of perturbed distance function is investigated in the Riemannian manifolds setting.

Suggested Citation

  • M. Farrokhiniya & A. Barani, 2020. "Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds," Journal of Global Optimization, Springer, vol. 77(3), pages 661-685, July.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:3:d:10.1007_s10898-020-00889-w
    DOI: 10.1007/s10898-020-00889-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00889-w
    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/s10898-020-00889-w?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. Jin-Hua Wang & Chong Li & Hong-Kun Xu, 2010. "Subdifferentials of perturbed distance functions in Banach spaces," Journal of Global Optimization, Springer, vol. 46(4), pages 489-501, April.
    2. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
    3. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
    4. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    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. G. C. Bento & J. X. Cruz Neto, 2013. "A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 125-137, October.
    2. João Carlos de O. Souza, 2018. "Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 745-760, December.
    3. Peng Zhang & Gejun Bao, 2018. "An Incremental Subgradient Method on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 711-727, March.
    4. G. C. Bento & J. X. Cruz Neto & P. S. M. Santos, 2013. "An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 108-124, October.
    5. Henri Bonnel & Léonard Todjihoundé & Constantin Udrişte, 2015. "Semivectorial Bilevel Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 464-486, November.
    6. Stevanovic Dalibor, 2016. "Common time variation of parameters in reduced-form macroeconomic models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(2), pages 159-183, April.
    7. Chiara Oostuizen & Sara S. Grobbelaar & Wouter G. Bam, 2018. "Project Portfolio Management Best Practice and Implementation: A South African Perspective," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-24, August.
    8. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    9. José M. Maisog & Andrew T. DeMarco & Karthik Devarajan & Stanley Young & Paul Fogel & George Luta, 2021. "Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    10. Lennart Bondesson, 2002. "On the Lévy Measure of the Lognormal and the LogCauchy Distributions," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 243-256, September.
    11. A. Fadlelmawla & M. Al-Otaibi, 2005. "Analysis of the Water Resources Status in Kuwait," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 19(5), pages 555-570, October.
    12. Shipra Agrawal & Yichuan Ding & Amin Saberi & Yinyu Ye, 2012. "Price of Correlations in Stochastic Optimization," Operations Research, INFORMS, vol. 60(1), pages 150-162, February.
    13. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    14. Duan, Jinyun & Li, Chenwei & Xu, Yue & Wu, Chia-Huei, 2017. "Transformational leadership and employee voice behavior: a Pygmalion mechanism," LSE Research Online Documents on Economics 68035, London School of Economics and Political Science, LSE Library.
    15. Hota, Monali & Bartsch, Fabian, 2019. "Consumer socialization in childhood and adolescence: Impact of psychological development and family structure," Journal of Business Research, Elsevier, vol. 105(C), pages 11-20.
    16. Heydari, Mohammadhossein & Sullivan, Kelly M., 2019. "Robust allocation of testing resources in reliability growth," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    17. Abernethy, Margaret A. & Vagnoni, Emidia, 2004. "Power, organization design and managerial behaviour," Accounting, Organizations and Society, Elsevier, vol. 29(3-4), pages 207-225.
    18. Dimitrios Letsios & Jeremy T. Bradley & Suraj G & Ruth Misener & Natasha Page, 2021. "Approximate and robust bounded job start scheduling for Royal Mail delivery offices," Journal of Scheduling, Springer, vol. 24(2), pages 237-258, April.
    19. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    20. Nearchou, Andreas C., 2006. "Meta-heuristics from nature for the loop layout design problem," International Journal of Production Economics, Elsevier, vol. 101(2), pages 312-328, June.

    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:77:y:2020:i:3:d:10.1007_s10898-020-00889-w. 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.