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Pointwise and global well-posedness in set optimization: a direct approach

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Abstract

The aim of this paper is to characterize some of the pointwise and global well-posedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.

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Acknowledgements

The authors thank the referees for their valuable suggestions that greatly helped to improve the paper. Research of C.S. Lalitha was supported by R&D Research Development Grant to University Faculty.

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Authors and Affiliations

  1. Department of Economics, Università degli Studi dell’Insubria, via Monte Generoso, 71, 21100, Varese, Italy

    Giovanni P. Crespi

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

    Mansi Dhingra

  3. Department of Mathematics, University of Delhi, South Campus, Benito Jaurez Road, New Delhi, 110021, India

    C. S. Lalitha

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  1. Giovanni P. Crespi
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  2. Mansi Dhingra
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  3. C. S. Lalitha
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Correspondence to C. S. Lalitha.

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Crespi, G.P., Dhingra, M. & Lalitha, C.S. Pointwise and global well-posedness in set optimization: a direct approach. Ann Oper Res 269, 149–166 (2018). https://doi.org/10.1007/s10479-017-2709-7

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  • DOI: https://doi.org/10.1007/s10479-017-2709-7

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