Scalarization and Optimality Conditions of E-Globally Proper Efficient Solution for Set-Valued Equilibrium Problems

Zhi-Ang Zhou and Min Kuang ()
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Zhi-Ang Zhou: College of Science, Chongqing University of Technology, Chongqing 400054, P. R. China
Min Kuang: College of Science, Chongqing University of Technology, Chongqing 400054, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 02, 1-16

Abstract: In this paper, our purpose is to use the improvement set to investigate the scalarization and optimality conditions of E-globally proper efficient solution for the set-valued equilibrium problems with constraints. First, the notion of E-globally proper efficient solution for set-valued equilibrium problems with constraints is introduced in locally convex Hausdorff topological spaces. Second, the linear scalarization theorems of E-globally proper efficient solution are derived. Finally, under the assumption of nearly E-subconvexlikeness, the Kuhn–Tucker and Lagrange optimality conditions for set-valued equilibrium problems with constraints are obtained in the sense of E-globally proper efficiency. Meanwhile, we give some examples to illustrate our results. The results obtained in this paper improve and generalize some known results in the literature.

Keywords: Set-valued equilibrium problems; E-globally proper efficient solution; nearly E-subconvexlikeness; optimality conditions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595922500099

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