IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p601-d750442.html
   My bibliography  Save this article

Optimality and Duality for DC Programming with DC Inequality and DC Equality Constraints

Author

Listed:
  • Yingrang Xu

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

  • Shengjie Li

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

Abstract

In this paper, a class of nondifferentiable DC programming with DC inequality and DC equality constraints are considered. Firstly, in terms of this special nondifferentiable DC constraint system, an appropriate relaxed constant rank constraint qualification is proposed and used to deduce one necessary optimality condition. Then, by adopting the convexification technique, another necessary optimality condition is obtained. Further, combined with the conjugate theory, the zero duality gap properties between the pairs of Wolfe and Mond-Weir type primal-dual problems are characterized, respectively.

Suggested Citation

  • Yingrang Xu & Shengjie Li, 2022. "Optimality and Duality for DC Programming with DC Inequality and DC Equality Constraints," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:601-:d:750442
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/601/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/601/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mengwei Xu & Jane J. Ye, 2020. "Relaxed constant positive linear dependence constraint qualification and its application to bilevel programs," Journal of Global Optimization, Springer, vol. 78(1), pages 181-205, September.
    2. D. H. Fang & Y. Zhang, 2018. "Extended Farkas’s Lemmas and Strong Dualities for Conic Programming Involving Composite Functions," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 351-376, February.
    3. 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.
    4. N. Dinh & J. Strodiot & V. Nguyen, 2010. "Duality and optimality conditions for generalized equilibrium problems involving DC functions," Journal of Global Optimization, Springer, vol. 48(2), pages 183-208, October.
    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. 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.
    2. N. Dinh & M. A. Goberna & M. A. López & T. H. Mo, 2017. "Farkas-Type Results for Vector-Valued Functions with Applications," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 357-390, May.
    3. Abdelghali Ammar & Mohamed Laghdir & Ahmed Ed-dahdah & Mohamed Hanine, 2023. "Approximate Subdifferential of the Difference of Two Vector Convex Mappings," Mathematics, MDPI, vol. 11(12), pages 1-14, June.
    4. 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.
    5. N. Dinh & V. Jeyakumar, 2014. "Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 1-22, April.
    6. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.

    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:gam:jmathe:v:10:y:2022:i:4:p:601-:d:750442. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.