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

Anveksha Moar (), Pradeep Kumar Sharma () and C. S. Lalitha ()
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Anveksha Moar: University of Delhi
Pradeep Kumar Sharma: University of Delhi South Campus
C. S. Lalitha: University of Delhi South Campus

Journal of Global Optimization, 2024, vol. 89, issue 4, No 10, 1099-1119

Abstract: 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.

Keywords: Set optimization; Set order relation; Nonlinear scalarizing function; Null set; Algebraic interior; 49J53; 65K10; 46N10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01385-1

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