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Strong subdifferentials: theory and applications in nonconvex optimization

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  • A. Kabgani

    (Urmia University of Technology)

  • F. Lara

    (Universidad de Tarapacá)

Abstract

A new subdifferential for dealing with nonconvex functions is provided in the following paper and the usual properties are presented as well. Furthermore, characterizations and optimality conditions for a point to be a solution for the nonconvex minimization problem are given. In particular, new KKT-type optimality conditions for nonconvex nonsmooth constraint optimization problems are developed. Moreover, a relationship with the proximity operator for lower semicontinuous quasiconvex functions is given and, as a consequence, the nonemptiness of this subdifferential for large classes of quasiconvex functions is ensured.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01149-9
    DOI: 10.1007/s10898-022-01149-9
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    References listed on IDEAS

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    8. 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.
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