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Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization

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Abstract

The aim of this paper is to establish scalar characterizations of minimal, weak minimal and strict minimal solutions in terms of a generalized oriented distance function defined on sets in real normed linear space with respect to a point in the space. Further, we study the lower and upper semicontinuity of the generalized oriented distance function.

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Acknowledgements

The authors are thankful to the anonymous referee for the valuable suggestions which improved the quality of the paper. This research for the first author is supported by CSIR, Senior Research Fellowship, India, National R &D Organization (Ack. No: 151012/2K18/1) and the second author is supported by MATRICS scheme of Department of Science and Technology, India.

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  1. Department of Mathematics, University of Delhi, Delhi, 110 007, India

    Khushboo

  2. Department of Mathematics, University of Delhi South Campus, Benito Juarez Road, New Delhi, 110 021, India

    C. S. Lalitha

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Khushboo, Lalitha, C.S. Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization. J Glob Optim 85, 235–249 (2023). https://doi.org/10.1007/s10898-022-01203-6

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  • DOI: https://doi.org/10.1007/s10898-022-01203-6

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