On scalarization and well-posedness in set optimization with a partial set order relation

被引：0
作者：
Sakshi Gupta
Rekha Gupta
Manjari Srivastava
机构：
[1] University of Delhi,Department of Mathematics
[2] University of Delhi,Department of Mathematics, Miranda House
来源：
Positivity | 2024年 / 28卷
关键词：
Set optimization; Partial set order relation; Scalarization function; Well-posedness; 49J53; 49K40; 90C48;
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摘要：
In this paper, a new scalarization function is introduced with respect to a partial set order relation established by Karaman et al. (Positivity 22(3):783–802, 2018). A few properties of this function are studied. Scalarization results and some characterizations for set of minimal and weak minimal solutions of a set optimization problem (SOP) in terms of the optimal solution set of the scalar optimization problem (P) are obtained using the newly defined scalarization function. Further, two types of well-posedness for (SOP) are introduced. Equivalence between the well-posedness of (SOP) with (P) is established and a few necessary conditions are obtained for the two well-posedness defined above.
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