Optimality conditions of approximate efficient solutions to set-valued vector equilibrium problems [集值向量均衡问题近似有效解的最优条件]

作者：Meng X.^*

来源：Journal of Zhejiang University (Science Edition), 2021, 48(4): 440-449.

DOI：10.3785/j.issn.1008-9497.2021.04.007

• Approximate efficient solutions
• Nearly cone-subconvexlike set-valued mapping
• Optimality conditions
• Set-valued vector equilibrium problems

In this paper, a kind of approximate efficient solutions to set-valued vector equilibrium problems with constraints is analyzed in real locally convex Hausdorff topological vector spaces, and the relationship between the efficient solutions and the approximate efficient solutions is discussed.Based on the concept of nearly cone-subconvexlike set-valued mapping, the optimality conditions of efficient solutions and approximate efficient solutions are established by applying the separation theorem for convex sets.Using analytic method, under the assumption of generalized convexity, the optimality necessary and sufficient conditions for both the Kuhn-Tucker-type and Lagrange-type approximate efficient solutions to the set-valued vector equilibrium problems are obtained.

• 单位
  南昌航空大学