IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v299y2022i1p35-45.html
   My bibliography  Save this article

Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization

Author

Listed:
  • Kabgani, Alireza
  • Soleimani-damaneh, Majid

Abstract

In this paper, we extend the concept of quasidifferential to a new notion called semi-quasidifferential. This generalization is motivated by the convexificator notion. Some important properties of semi-quasidifferentials are established. The relationship between semi-quasidifferentials and the Clarke subdifferential is studied, and a mean value theorem in terms of semi-quasidifferentials is proved. It is shown that this notion is helpful to investigate nonsmooth optimization problems even when the objective and/or constraint functions are discontinuous. Considering a multiobjective optimization problem, a characterization of some cones related to the feasible set is provided. They are used for deriving necessary and sufficient optimality conditions. We close the paper by obtaining optimality conditions in multiobjective optimization in terms of semi-quasidifferentials. Some outcomes of the current work generalize the related results existing in the literature.

Suggested Citation

  • Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.
    • Handle: RePEc:eee:ejores:v:299:y:2022:i:1:p:35-45
    DOI: 10.1016/j.ejor.2021.10.063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721009267
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.10.063?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. Nader Kanzi & Majid Soleimani-damaneh, 2020. "Characterization of the weakly efficient solutions in nonsmooth quasiconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 77(3), pages 627-641, July.
    2. Qu, Shaojian & Liu, Chen & Goh, Mark & Li, Yijun & Ji, Ying, 2014. "Nonsmooth multiobjective programming with quasi-Newton methods," European Journal of Operational Research, Elsevier, vol. 235(3), pages 503-510.
    3. Majid E. Abbasov, 2017. "Comparison Between Quasidifferentials and Exhausters," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 59-75, October.
    4. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
    5. Chieu, N.H. & Jeyakumar, V. & Li, G. & Mohebi, H., 2018. "Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation," European Journal of Operational Research, Elsevier, vol. 265(1), pages 19-25.
    6. Fakhar, Majid & Mahyarinia, Mohammad Reza & Zafarani, Jafar, 2018. "On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 265(1), pages 39-48.
    7. T. Antczak, 2016. "Optimality Conditions in Quasidifferentiable Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 708-725, November.
    8. Brito, A.S. & Cruz Neto, J.X. & Santos, P.S.M. & Souza, S.S., 2017. "A relaxed projection method for solving multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 256(1), pages 17-23.
    9. M. V. Dolgopolik, 2020. "New global optimality conditions for nonsmooth DC optimization problems," Journal of Global Optimization, Springer, vol. 76(1), pages 25-55, January.
    10. Papa Quiroz, E.A. & Mallma Ramirez, L. & Oliveira, P.R., 2015. "An inexact proximal method for quasiconvex minimization," European Journal of Operational Research, Elsevier, vol. 246(3), pages 721-729.
    11. Vieira, D.A.G. & Lisboa, A.C., 2019. "A cutting-plane method to nonsmooth multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 822-829.
    12. V. Jeyakumar & D.T. LUC, 2008. "Nonsmooth Vector Functions and Continuous Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-73717-1, June.
    13. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.
    14. Alireza Kabgani & Majid Soleimani-damaneh & Moslem Zamani, 2017. "Optimality conditions in optimization problems with convex feasible set using convexificators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 103-121, August.
    15. V. Jeyakumar & D. T. Luc, 1999. "Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 599-621, June.
    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. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.

    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. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.
    2. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.
    3. Vivek Laha & Harsh Narayan Singh, 2023. "On quasidifferentiable mathematical programs with equilibrium constraints," Computational Management Science, Springer, vol. 20(1), pages 1-20, December.
    4. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.
    5. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    6. Felipe Lara & Alireza Kabgani, 2021. "On global subdifferentials with applications in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 81(4), pages 881-900, December.
    7. Felipe Serrano & Robert Schwarz & Ambros Gleixner, 2020. "On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm," Journal of Global Optimization, Springer, vol. 78(1), pages 161-179, September.
    8. Alireza Kabgani & Majid Soleimani-damaneh & Moslem Zamani, 2017. "Optimality conditions in optimization problems with convex feasible set using convexificators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 103-121, August.
    9. Do Luu & Tran Thi Mai, 2018. "Optimality and duality in constrained interval-valued optimization," 4OR, Springer, vol. 16(3), pages 311-337, September.
    10. 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.
    11. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.
    12. Mingcheng Zuo & Yuan Xue, 2024. "Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization," Mathematics, MDPI, vol. 12(6), pages 1-24, March.
    13. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.
    14. Vaithilingam Jeyakumar & Guoyin Li, 2017. "Exact Conic Programming Relaxations for a Class of Convex Polynomial Cone Programs," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 156-178, January.
    15. Do Luu, 2016. "Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 643-665, November.
    16. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
    17. M. Alavi Hejazi & N. Movahedian, 2020. "A New Abadie-Type Constraint Qualification for General Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 86-101, July.
    18. Do Luu, 2014. "Necessary and Sufficient Conditions for Efficiency Via Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 510-526, February.
    19. J. Dutta & S. Chandra, 2002. "Convexifactors, Generalized Convexity, and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 41-64, April.
    20. M. Alavi Hejazi & N. Movahedian & S. Nobakhtian, 2018. "On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 778-799, 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:eee:ejores:v:299:y:2022:i:1:p:35-45. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.