Abstract
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.
Supported by the National Nature Science Foundation of China (12171061), the Science and Technology Research Program of Chongqing Education Commission (KJZD-K202001104) and Chongqing Graduate Innovation Project (CYS22671).
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The authors would like to express their thanks to two anonymous referees for their valuable comments and suggestions.
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Zhou, Z., Wei, W., Zhao, K. (2024). Weakly Nondominated Solutions of Set-Valued Optimization Problems with Variable Ordering Structures in Linear Spaces. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14461. Springer, Cham. https://doi.org/10.1007/978-3-031-49611-0_13
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