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Well-setness and scalarization in set optimization

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Abstract

In this paper, we consider a notion of global well-setness for a set optimization problem using the excess function. We give sufficient conditions for well-setness and establish Dontchev–Zolezzi type measure for well-setness. Moreover, we relate this notion with well-setness notion for a scalar problem obtained by using generalized Gerstewitz’s function.

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Acknowledgments

The authors would like to thank the anonymous referees for providing many helpful suggestions which improved the paper. Research of C.S. Lalitha was supported by R&D Doctoral Research Programme Fund for University faculty.

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Authors and Affiliations

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

    Mansi Dhingra

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

    C. S. Lalitha

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  1. Mansi Dhingra
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  2. C. S. Lalitha
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Correspondence to Mansi Dhingra.

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Dhingra, M., Lalitha, C.S. Well-setness and scalarization in set optimization. Optim Lett 10, 1657–1667 (2016). https://doi.org/10.1007/s11590-015-0942-z

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  • DOI: https://doi.org/10.1007/s11590-015-0942-z

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