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Nonlinear scalarization in set optimization based on the concept of null set

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Abstract

The aim of this paper is to introduce a nonlinear scalarization function in set optimization based on the concept of null set which was introduced by Wu (J Math Anal Appl 472(2):1741–1761, 2019). We introduce a notion of pseudo algebraic interior of a set and define a weak set order relation using the concept of null set. We investigate several properties of this nonlinear scalarization function. Further, we characterize the set order relations and investigate optimality conditions for solution sets in set optimization based on the concept of null set. Finally, a numerical example is provided to compute a weak minimal solution using this nonlinear scalarization function.

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Acknowledgements

The authors are grateful to the handling editor and the anonymous referees for their valuable comments and suggestions which helped to improve the previous draft of the paper.

Funding

The research work of the first author is supported by the University Grants Commission (UGC) [Ref. No.: 191620044526], New Delhi, India. The research work of the second author is supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship No. F.4-2/2006 (BSR)/MA/19-20/0040. The research work of the third author is supported by the research grant under the Faculty Research Programme of the IoE scheme, University of Delhi (Grant Number IoE/2023-24/12/FRP).

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Author notes

  1. Anveksha Moar, Pradeep Kumar Sharma and C. S. Lalitha have contributed equally to this work.

Authors and Affiliations

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

    Anveksha Moar

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

    Pradeep Kumar Sharma & C. S. Lalitha

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  1. Anveksha Moar
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  2. Pradeep Kumar Sharma
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  3. C. S. Lalitha
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Correspondence to C. S. Lalitha.

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Moar, A., Sharma, P.K. & Lalitha, C.S. Nonlinear scalarization in set optimization based on the concept of null set. J Glob Optim (2024). https://doi.org/10.1007/s10898-024-01385-1

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