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Pointwise well-posedness and scalarization in set optimization

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Abstract

In this paper, some notions of pointwise well-posedness for set optimization problems are introduced. Some relationships among these notions are established. Using a new nonlinear scalarization function, pointwise well-posed set optimization problems are characterized by means of a family of Tykhonov well-posed scalar optimization problems. Also, three classes of well-posed set optimization problems are identified.

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Acknowledgments

The authors would like to express their gratitude to the anonymous referees for their helpful comments on the first version of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Avenue, 15914, Tehran, Iran

    S. Khoshkhabar-amiranloo & E. Khorram

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  1. S. Khoshkhabar-amiranloo
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  2. E. Khorram
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Correspondence to E. Khorram.

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Khoshkhabar-amiranloo, S., Khorram, E. Pointwise well-posedness and scalarization in set optimization. Math Meth Oper Res 82, 195–210 (2015). https://doi.org/10.1007/s00186-015-0509-x

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