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Approximate Weak Minimal Solutions of Set-Valued Optimization Problems

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Abstract

This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria. The relationships between various concepts of approximate weak minimal solutions are investigated. Some topological properties and existence theorems of these solutions are given. It is shown that for set-valued optimization problems with upper (outer) cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed. By using the polar cone and two scalarization processes, some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.

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Acknowledgements

I would like to express my gratitude to the anonymous referees for their helpful comments and providing helpful suggestions which improved the paper.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences, Tehran, Iran

    S. Khoshkhabar-amiranloo

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  1. S. Khoshkhabar-amiranloo
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Correspondence to S. Khoshkhabar-amiranloo.

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There are no conflicts of interest regarding the publication of this paper.

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I confirm sole responsibility for the study conception, data collection, analysis and manuscript preparation.

Additional information

This research was in part supported by a Grant from Institute for Research in Fundamental Sciences (No. 96580048)

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Khoshkhabar-amiranloo, S. Approximate Weak Minimal Solutions of Set-Valued Optimization Problems. J. Oper. Res. Soc. China 11, 673–692 (2023). https://doi.org/10.1007/s40305-022-00401-z

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  • DOI: https://doi.org/10.1007/s40305-022-00401-z

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