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Characterizations of the solution set for tangentially convex optimization problems

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Abstract

In convex optimization problems, characterizations of the solution set in terms of the classical subdifferentials have been investigated by Mangasarian. In quasiconvex optimization problems, characterizations of the solution set for quasiconvex programming in terms of the Greenberg–Pierskalla subdifferentials were given by Suzuki and Kuroiwa. In this paper, our attention focuses on the class of tangentially convex functions. Indeed, we study characterizations of the solution set for tangentially convex optimization problems in terms of subdifferentials. For this purpose, we use tangential subdifferentials and the Greenberg-Pierskalla subdifferentials and present necessary and sufficient optimality conditions for tangentially convex optimization problems. As a consequence, we investigate characterizations of the solution set in terms of tangential subdifferentials and the Greenberg–Pierskalla subdifferentials for tangentially convex optimization problems. Moreover, we compare our results with previous ones.

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Acknowledgements

The authors are very grateful to the three anonymous referees and the Associate Editor for their helpful comments and valuable suggestions and criticism regarding an earlier version of this paper. The comments of the referees and the Associate Editor were very useful and they helped us to improve the paper significantly. The second author was partially supported by Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Iran [grant no: 99/3668].

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Authors and Affiliations

  1. Department of Mathematics, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran

    M. Beni-Asad & H. Mohebi

  2. Graduate University of Advanced Technology, 7616914111, Kerman, Iran

    H. Mohebi

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  1. M. Beni-Asad
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  2. H. Mohebi
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Correspondence to H. Mohebi.

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Beni-Asad, M., Mohebi, H. Characterizations of the solution set for tangentially convex optimization problems. Optim Lett 17, 1027–1048 (2023). https://doi.org/10.1007/s11590-022-01911-8

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