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On robustness for set-valued optimization problems

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Abstract

In the recent past, finding robust solutions for optimization problems contaminated with uncertainties has been topical and has been investigated in the literature for scalar and multi-objective/vector-valued optimization problems. In this paper, we introduce various types of robustness concept for set-valued optimization, such as min–max set robustness, optimistic set robustness, highly set robustness, flimsily set robustness, multi-scenario set robustness. We study some existence results for corresponding concepts of solution and establish some relationship among them.

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Acknowledgements

The authors are indebted to the referees for their invaluable suggestions and comments that have substantially improved the paper. The first author thanks National Board for Higher Mathematics, India (Ref. No.: 2/39(2)/2015/NBHM/R& D-II/7463) for financial assistance. The second author thanks the Department of Science and Technology (SERB), India, for the financial support under the MATRICS scheme (MTR/2017/000128).

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  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    Kuntal Som & V. Vetrivel

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  1. Kuntal Som
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  2. V. Vetrivel
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Som, K., Vetrivel, V. On robustness for set-valued optimization problems. J Glob Optim 79, 905–925 (2021). https://doi.org/10.1007/s10898-020-00959-z

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