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

Author

Listed:
  • Anveksha Moar

    (University of Delhi)

  • Pradeep Kumar Sharma

    (University of Delhi South Campus)

  • C. S. Lalitha

    (University of Delhi South Campus)

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.

Suggested Citation

  • Anveksha Moar & Pradeep Kumar Sharma & C. S. Lalitha, 2024. "Nonlinear scalarization in set optimization based on the concept of null set," Journal of Global Optimization, Springer, vol. 89(4), pages 1099-1119, August.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:4:d:10.1007_s10898-024-01385-1
    DOI: 10.1007/s10898-024-01385-1
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    References listed on IDEAS

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    1. Adan, M. & Novo, V., 2003. "Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness," European Journal of Operational Research, Elsevier, vol. 149(3), pages 641-653, September.
    2. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    3. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, December.
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