Directional Derivative and Subgradient of Cone-Convex Set-Valued Mappings with Applications in Set Optimization Problems

doi:10.1007/s40305-023-00454-8

Abstract

Abstract: In this paper, we introduce a new directional derivative and subgradient of set-valued mappings by using a nonlinear scalarizing function. We obtain some properties of directional derivative and subgradient for cone-convex set-valued mappings. As applications, we present necessary and sufficient optimality conditions for set optimization problems and show that the local weak l-minimal solutions of set optimization problems are the global weak l-minimal solutions of set optimization problems under the assumption that the objective mapping is cone-convex.

Key words: Set optimization problem, Nonlinear scalarizing function, Directional derivative, Subgradient

CLC Number:

49J53
90C29

Yu Han. Directional Derivative and Subgradient of Cone-Convex Set-Valued Mappings with Applications in Set Optimization Problems[J]. Journal of the Operations Research Society of China, 2024, 12(4): 1103-1125.

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References

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