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A Note on Pointwise Well-Posedness of Set-Valued Optimization Problems

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Abstract

Well-posedness for optimization problems is a well-known notion and has been studied extensively for scalar, vector, and set-valued optimization problems. For the set-valued case, there are many subdivisions: firstly in terms of pointwise notion and global notion and secondly in terms of the solution concepts, like the vector approach, the set-relation approach, etc. Various definitions of pointwise well-posedness for a set-valued optimization problem in the set-relation approach have been proposed in the literature. Here we do a comparative study and suggest modifications in some existing results. We also introduce a new pointwise well-posedness and discuss its properties and connection with others.

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Acknowledgements

The authors are indebted to the anonymous referees for their valuable comments and suggestions that have helped to improve 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 & Vellaichamy Vetrivel

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  1. Kuntal Som
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  2. Vellaichamy Vetrivel
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Communicated by Antonino Maugeri.

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Som, K., Vetrivel, V. A Note on Pointwise Well-Posedness of Set-Valued Optimization Problems. J Optim Theory Appl 192, 628–647 (2022). https://doi.org/10.1007/s10957-021-01981-1

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