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New vectorial versions of Takahashi’s nonconvex minimization problem

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Abstract

In this article, some new vectorial versions of Takahashi’s nonconvex minimization theorem, which involve algebraic notions instead of topological notions, are established. A nonlinear separation theorem, which extends the result derived by Gerth and Weidner (JAMA 67:297–320, 1990) to general linear spaces (not necessarily endowed with a topology), is proved. Some examples, in order to illustrate and compare the results of this article with the corresponding known results from the literature, are provided.

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Acknowledgements

The authors would like to thank anonymous reviewer for valuable suggestions and remarks.

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  1. Department of Mathematics, Faculty of Science, Razi University, P.O. Box 67149-67346, Kermanshah, Iran

    B. Khazayel & A. Farajzadeh

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  1. B. Khazayel
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  2. A. Farajzadeh
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Correspondence to A. Farajzadeh.

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Khazayel, B., Farajzadeh, A. New vectorial versions of Takahashi’s nonconvex minimization problem. Optim Lett 15, 847–858 (2021). https://doi.org/10.1007/s11590-019-01521-x

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