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On Benson’s scalarization in multiobjective optimization

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Abstract

In this paper, a popular scalarization problem in multiobjective optimization, introduced by Benson, is considered. In the literature it was proved that, under convexity assumption, the set of properly efficient points is empty when the Benson’s problem is unbounded. In this paper, it is shown that this result is still valid in general case without convexity assumption.

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Acknowledgments

The authors would like to express their gratitude to anonymous referee and handling editor for their helpful comments on the first version of this paper. This research was in part supported by a Grant from IPM (No. 94260124).

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Majid Soleimani-damaneh & Moslem Zamani

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), 19395-5746, Tehran, Iran

    Majid Soleimani-damaneh & Moslem Zamani

Authors
  1. Majid Soleimani-damaneh
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  2. Moslem Zamani
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Correspondence to Majid Soleimani-damaneh.

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Soleimani-damaneh, M., Zamani, M. On Benson’s scalarization in multiobjective optimization. Optim Lett 10, 1757–1762 (2016). https://doi.org/10.1007/s11590-016-0999-3

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  • DOI: https://doi.org/10.1007/s11590-016-0999-3

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