IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v16y2018i3d10.1007_s10288-017-0369-8.html
   My bibliography  Save this article

Optimality and duality in constrained interval-valued optimization

Author

Listed:
  • Do Luu

    (Thang Long University
    Vietnam Academy of Science and Technology)

  • Tran Thi Mai

    (Thai Nguyen University of Economics and Business Administration)

Abstract

Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.

Suggested Citation

  • Do Luu & Tran Thi Mai, 2018. "Optimality and duality in constrained interval-valued optimization," 4OR, Springer, vol. 16(3), pages 311-337, September.
    • Handle: RePEc:spr:aqjoor:v:16:y:2018:i:3:d:10.1007_s10288-017-0369-8
    DOI: 10.1007/s10288-017-0369-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-017-0369-8
    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/s10288-017-0369-8?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. 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.
    2. A. K. Bhurjee & G. Panda, 2016. "Sufficient optimality conditions and duality theory for interval optimization problem," Annals of Operations Research, Springer, vol. 243(1), pages 335-348, August.
    3. 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. Tran Su, 2024. "Optimality analysis for $$\epsilon $$ ϵ -quasi solutions of optimization problems via $$\epsilon $$ ϵ -upper convexificators: a dual approach," Journal of Global Optimization, Springer, vol. 90(3), pages 651-669, November.
    2. Tran Van Su, 2023. "Optimality and duality for nonsmooth mathematical programming problems with equilibrium constraints," Journal of Global Optimization, Springer, vol. 85(3), pages 663-685, March.
    3. Fabiola Roxana Villanueva & Valeriano Antunes Oliveira, 2022. "Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 896-923, September.
    4. B. Japamala Rani & Krishna Kummari, 2023. "Duality for fractional interval-valued optimization problem via convexificator," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 481-500, March.

    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. Tran Su, 2024. "Optimality analysis for $$\epsilon $$ ϵ -quasi solutions of optimization problems via $$\epsilon $$ ϵ -upper convexificators: a dual approach," Journal of Global Optimization, Springer, vol. 90(3), pages 651-669, November.
    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. 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.
    4. 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.
    5. Tran Van Su, 2018. "New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces," 4OR, Springer, vol. 16(2), pages 173-198, June.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Muhammad Bilal Khan & Savin Treanțǎ & Mohamed S. Soliman & Kamsing Nonlaopon & Hatim Ghazi Zaini, 2022. "Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    12. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    13. 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.
    14. 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.
    15. B. Japamala Rani & Krishna Kummari, 2023. "Duality for fractional interval-valued optimization problem via convexificator," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 481-500, March.
    16. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.
    17. 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.
    18. X. F. Li & J. Z. Zhang, 2010. "Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 373-386, May.
    19. D.T. Luc & M.A. Noor, 2003. "Local Uniqueness of Solutions of General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 103-119, April.
    20. 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.

    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:aqjoor:v:16:y:2018:i:3:d:10.1007_s10288-017-0369-8. 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.