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Strong subdifferentials: theory and applications in nonconvex optimization

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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.

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Acknowledgements

The authors wishes to thank the reviewer for his/her comments and remarks that improved this paper.

Funding

This research was partially supported by Iran National Science Foundation (INSF) (No. 99001508) (Kabgani) and by ANID-Chile under project Fondecyt Regular 1220379 (Lara).

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Authors and Affiliations

  1. Mathematics Group, Department of Environment, Urmia University of Technology, Urmia, Iran

    A. Kabgani

  2. Departamento de Matemática, Facultad de Ciencias, Universidad de Tarapacá, Arica, Chile

    F. Lara

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  1. A. Kabgani
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  2. F. Lara
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Both authors contributed equally to the study conception and design.

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Correspondence to F. Lara.

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Kabgani, A., Lara, F. Strong subdifferentials: theory and applications in nonconvex optimization. J Glob Optim 84, 349–368 (2022). https://doi.org/10.1007/s10898-022-01149-9

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