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Convergence, Scalarization and Continuity of Minimal Solutions in Set Optimization

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Abstract

The paper deals with the study of two different aspects of stability in the given space as well as the image space, where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space. The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painlevé–Kuratowski set convergence of solution sets of the perturbed problems in the given space. The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems. The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable suggestions and comments, which led to improvement of the paper.

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Authors and Affiliations

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

    Karuna

  2. Department of Mathematics, University of Delhi South Campus, New Delhi, Delhi, 110021, India

    C. S. Lalitha

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  1. Karuna
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Both the authors have made equal contributions in the paper.

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Correspondence to C. S. Lalitha.

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The research of the second author is supported by MATRICS scheme of Department of Science and Technology, India (No. MTR/2017/00016).

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Karuna, Lalitha, C.S. Convergence, Scalarization and Continuity of Minimal Solutions in Set Optimization. J. Oper. Res. Soc. China (2022). https://doi.org/10.1007/s40305-022-00440-6

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  • DOI: https://doi.org/10.1007/s40305-022-00440-6

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