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

Zhiang Zhou (), Kehui Liang () and Qamrul Hasan Ansari ()
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Zhiang Zhou: Chongqing University of Technology
Kehui Liang: Chongqing University of Technology
Qamrul Hasan Ansari: Chongqing University of Technology

Mathematical Methods of Operations Research, 2025, vol. 101, issue 1, No 6, 134 pages

Abstract: 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.

Keywords: Equilibrium problems; Benson properly efficient solutions; Recession cone; Optimality conditions; 26B25; 90C26; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00887-2

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