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Nonlinear scalarization functions and polar cone in set optimization

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Abstract

In this paper, some new nonlinear scalarization functions are introduced and some of their properties are investigated. Using these functions and the polar cone, we characterize set optimal solutions of set optimization problems. Also, some relationships between the cone-convexity (resp. cone-quasiconvexity) of a set-valued map and the convexity (resp. quasiconvexity) of its scalarized versions are established.

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Acknowledgments

The authors are grateful 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, Tehran, 15914, Iran

    S. Khoshkhabar-amiranloo & E. Khorram

  2. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran

    M. Soleimani-damaneh

Authors
  1. S. Khoshkhabar-amiranloo
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  2. E. Khorram
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  3. M. Soleimani-damaneh
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Correspondence to E. Khorram.

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Khoshkhabar-amiranloo, S., Khorram, E. & Soleimani-damaneh, M. Nonlinear scalarization functions and polar cone in set optimization. Optim Lett 11, 521–535 (2017). https://doi.org/10.1007/s11590-016-1027-3

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  • DOI: https://doi.org/10.1007/s11590-016-1027-3

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