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On scalarization and well-posedness in set optimization with a partial set order relation

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Abstract

In this paper, a new scalarization function is introduced with respect to a partial set order relation established by Karaman et al. (Positivity 22(3):783–802, 2018). A few properties of this function are studied. Scalarization results and some characterizations for set of minimal and weak minimal solutions of a set optimization problem (SOP) in terms of the optimal solution set of the scalar optimization problem (P) are obtained using the newly defined scalarization function. Further, two types of well-posedness for (SOP) are introduced. Equivalence between the well-posedness of (SOP) with (P) is established and a few necessary conditions are obtained for the two well-posedness defined above.

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Acknowledgements

The authors are grateful to Ms. Meenakshi Gupta for giving suggestions which improved few results particularly related to optimality results in our paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Sakshi Gupta

  2. Department of Mathematics, Miranda House, University of Delhi, Delhi, 110007, India

    Rekha Gupta & Manjari Srivastava

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  1. Sakshi Gupta
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  2. Rekha Gupta
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  3. Manjari Srivastava
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All the authors conceptualized the contents and also reviewed the manuscript after completion. First author (SG) typed the manuscript, second author (RG) edited the manuscript and third author (MS) did the final checking.

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Correspondence to Sakshi Gupta.

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Gupta, S., Gupta, R. & Srivastava, M. On scalarization and well-posedness in set optimization with a partial set order relation. Positivity 28, 1 (2024). https://doi.org/10.1007/s11117-023-01018-z

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