Weakly Nondominated Solutions of Set-Valued Optimization Problems with Variable Ordering Structures in Linear Spaces

In this paper, weakly nondominated solutions of set-valued optimization problems with variable ordering structures are investigated in linear spaces. Firstly, the notion of weakly nondominated element of a set with a variable ordering structure is introduced in linear spaces, and the relationship between weakly nondominated element and nondominated element is also given. Secondly, under the assumption of nearly \(\mathcal {C}(y)\) -subconvexlikeness of set-valued maps, scalarization theorems of weakly nondominated solutions for unconstrained set-valued optimization problems are established. Finally, two duality theorems of constrained set-valued optimization problems are obtained. Some examples are given to illustrate our results. The results obtained in this paper improve and generalize some known results in the literatures.