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<p>In this paper, we investigate Benson proper subdifferential of the set-valued map in real linear spaces. Firstly, based on the notion of Benson properly efficient point, we introduce Benson proper subdifferential of the set-valued map and study the existence conditions of Benson proper subdifferential in real linear spaces. Secondly, Moreau-Rockafellar type theorem characterized by Benson proper subdifferential is established in real linear spaces. Finally, as the applications, we establish some optimality conditions of the set-valued optimization problem involving Benson proper subdifferential in real linear spaces. The results obtained in this paper extend some known results in the literature from topological spaces to real linear spaces.</p>

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Proper Subdifferential of Set-Valued Maps and its Applications in Linear Spaces

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Zhiang Zhou,
  • Zhongcheng Deng,
  • Caiping Liu,
  • Kequan Zhao

摘要

In this paper, we investigate Benson proper subdifferential of the set-valued map in real linear spaces. Firstly, based on the notion of Benson properly efficient point, we introduce Benson proper subdifferential of the set-valued map and study the existence conditions of Benson proper subdifferential in real linear spaces. Secondly, Moreau-Rockafellar type theorem characterized by Benson proper subdifferential is established in real linear spaces. Finally, as the applications, we establish some optimality conditions of the set-valued optimization problem involving Benson proper subdifferential in real linear spaces. The results obtained in this paper extend some known results in the literature from topological spaces to real linear spaces.