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

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  • School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, Jiangxi, China

Received date: 2020-10-25

  Online published: 2024-12-12

Supported by

This work was supported by the National Natural Science Foundation of China (11801257).

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.

Cite this article

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 . DOI: 10.1007/s40305-023-00454-8

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