IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v200y2024i2d10.1007_s10957-023-02301-5.html
   My bibliography  Save this article

Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds

Author

Listed:
  • Balendu Bhooshan Upadhyay

    (Indian Institute of Technology Patna)

  • Arnav Ghosh

    (Indian Institute of Technology Patna)

  • Savin Treanţă

    (University Politehnica of Bucharest
    54 Splaiul Independentei
    University Politehnica of Bucharest)

Abstract

This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush–Kuhn–Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.

Suggested Citation

  • Balendu Bhooshan Upadhyay & Arnav Ghosh & Savin Treanţă, 2024. "Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 794-819, February.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:2:d:10.1007_s10957-023-02301-5
    DOI: 10.1007/s10957-023-02301-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02301-5
    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/s10957-023-02301-5?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Sheng-lan Chen & Nan-Jing Huang & Donal O'Regan, 2014. "Geodesic B -Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, March.
    2. X. F. Li, 2000. "Constraint Qualifications in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 373-398, August.
    3. Mohammad Mahdi Karkhaneei & Nezam Mahdavi-Amiri, 2019. "Nonconvex Weak Sharp Minima on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 85-104, October.
    4. O. Stein, 2004. "On Constraint Qualifications in Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 647-671, June.
    5. V. Preda & I. Chiţescu, 1999. "On Constraint Qualification in Multiobjective Optimization Problems: Semidifferentiable Case," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 417-433, February.
    6. Sheng-lan Chen & Nan-Jing Huang & Donal O′Regan, 2014. "Geodesic B‐Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    7. Balendu Bhooshan Upadhyay & Arnav Ghosh, 2023. "On Constraint Qualifications for Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 1-35, October.
    8. 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.
    9. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    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. Balendu Bhooshan Upadhyay & Shubham Kumar Singh & Ioan Stancu-Minasian, 2024. "Constraint Qualifications and Optimality Conditions for Nonsmooth Semidefinite Multiobjective Programming Problems with Mixed Constraints Using Convexificators," Mathematics, MDPI, vol. 12(20), pages 1-21, October.
    2. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    3. Do Van Luu & Manh-Hung Nguyen, 2006. "On alternative theorems and necessary conditions for efficiency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00112454, HAL.
    4. Balendu Bhooshan Upadhyay & Arnav Ghosh & Savin Treanţă, 2024. "Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 89(3), pages 723-744, July.
    5. Ehtesham Akhter & Mohd Bilal & Musavvir Ali, 2025. "A Study of Geodesic ( E , F )-Preinvex Functions on Riemannian Manifolds," Mathematics, MDPI, vol. 13(6), pages 1-9, March.
    6. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2023. "Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(2), pages 355-377, December.
    7. Xiaoqi Yang & Zhangyou Chen & Jinchuan Zhou, 2016. "Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 984-1012, June.
    8. Hui Huang & Haole Zhu, 2022. "Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints," Mathematics, MDPI, vol. 10(23), pages 1-18, December.
    9. Balendu Bhooshan Upadhyay & Arnav Ghosh, 2023. "On Constraint Qualifications for Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 1-35, October.
    10. Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    11. Gabriel Ruiz-Garzón & Rafaela Osuna-Gómez & Antonio Rufián-Lizana & Beatriz Hernández-Jiménez, 2020. "Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities," Mathematics, MDPI, vol. 8(12), pages 1-19, December.
    12. Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.
    13. J. J. Ye & S. Y. Wu, 2008. "First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 419-434, May.
    14. S. Nobakhtian, 2008. "Generalized (F,ρ)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 61-68, January.
    15. Erik Papa Quiroz & Antoine Soubeyran, 2024. "Local proximal algorithms in Riemannian manifolds: Application to the behavioral traveler's problem," Post-Print hal-04930974, HAL.
    16. Regina S. Burachik & M. M. Rizvi, 2012. "On Weak and Strong Kuhn–Tucker Conditions for Smooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 477-491, November.
    17. Jian Lv & Li-Ping Pang & Fan-Yun Meng, 2018. "A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information," Journal of Global Optimization, Springer, vol. 70(3), pages 517-549, March.
    18. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    19. G. C. Bento & J. X. Cruz Neto & L. V. Meireles & A. Soubeyran, 2022. "Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm," Annals of Operations Research, Springer, vol. 316(2), pages 1425-1443, September.
    20. Manh-Hung Nguyen & Do Van Luu, 2006. "On necessary conditions for efficiency in directionally differentiable optimization problems," Post-Print halshs-00118977, HAL.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:joptap:v:200:y:2024:i:2:d:10.1007_s10957-023-02301-5. 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.