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Optimality conditions for Benson proper efficiency of set-valued equilibrium problems

Author

Listed:
  • Zhiang Zhou

    (Chongqing University of Technology)

  • Kehui Liang

    (Chongqing University of Technology)

  • Qamrul Hasan Ansari

    (Chongqing University of Technology
    King Fahd University of Petroleum and Minerals)

Abstract

In this paper, we utilize the improvement set and the recession cone to introduce the concept of $$E_{\infty }$$ E ∞ -Benson properly efficient solution of the set-valued equilibrium problems and set-valued optimization problems. We establish scalarization optimality conditions, both linear and nonlinear, for $$E_{\infty }$$ E ∞ -Benson proper efficiency of the set-valued equilibrium problems and also of the set-valued optimization problems. Based on the linear scalarization, we derive Lagrange multiplier optimality conditions for $$E_{\infty }$$ E ∞ -Benson proper efficiency of the set-valued equilibrium problems and also of the set-valued optimization problems. Several results obtained in this paper are illustrated by examples. The results obtained in this paper improve and generalize some known results in the literature.

Suggested Citation

  • Zhiang Zhou & Kehui Liang & Qamrul Hasan Ansari, 2025. "Optimality conditions for Benson proper efficiency of set-valued equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(1), pages 111-134, February.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:1:d:10.1007_s00186-025-00887-2
    DOI: 10.1007/s00186-025-00887-2
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    References listed on IDEAS

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