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Approximate Subdifferential of the Difference of Two Vector Convex Mappings

Author

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  • Abdelghali Ammar

    (Department of Computer Engineering, Networks and Telecommunications, National School of Applied Sciences, Cadi Ayyad University, BP. 63, Safi 46000, Morocco
    These authors contributed equally to this work.)

  • Mohamed Laghdir

    (Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, BP. 20, El Jadida 24000, Morocco
    These authors contributed equally to this work.)

  • Ahmed Ed-dahdah

    (Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, BP. 20, El Jadida 24000, Morocco
    These authors contributed equally to this work.)

  • Mohamed Hanine

    (Department of Telecommunications, Networks, and Informatics, National School of Applied Sciences, Chouaib Doukkali University, El Jadida 24000, Morocco
    These authors contributed equally to this work.)

Abstract

This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2718-:d:1171938
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    References listed on IDEAS

    as
    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. M. Volle, 2002. "Duality Principles for Optimization Problems Dealing with the Difference of Vector-Valued Convex Mappings," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 223-241, July.
    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.
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