文章摘要
孟旭东,万德龙.含参集值向量均衡问题近似解映射的Lipschitz连续性[J].,2019,59(4):434-440
含参集值向量均衡问题近似解映射的Lipschitz连续性
Lipschitz continuity of approximate solution mapping for parametric set-valued vector equilibrium problems
  
DOI:10.7511/dllgxb201904015
中文关键词: Lipschitz连续性  集值向量均衡问题  近似有效解  向量优化问题
英文关键词: Lipschitz continuity  set-valued vector equilibrium problem  approximate efficient solutions  vector optimization problem
基金项目:国家自然科学基金资助项目(11201216);江西省教育厅科学技术重点研究项目(GJJ181565);江西省教育厅科学技术研究项目(GJJ161597GJJ181567)
作者单位
孟旭东,万德龙  
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中文摘要:
      在赋范线性空间中研究了含参集值向量均衡问题.在引入含参集值向量均衡问题近似有效解的基础上,讨论了含参集值向量均衡问题近似解映射的Lipschitz连续性.借助标量化方法,得到了含参集值向量均衡问题近似解映射的Lipschitz连续的充分性定理.作为应用,研究了含参集值向量优化问题近似解映射的Lipschitz连续性,给出了含参集值向量优化问题近似解映射的Lipschitz连续的充分性条件.
英文摘要:
      The parametric set-valued vector equilibrium problems are studied in normed linear space.On the basis of introducing the approximate efficient solution of parametric set-valued vector equilibrium problems, the Lipschitz continuity of approximate solution mapping for parametric set-valued vector equilibrium problems is discussed.Sufficient theorem of the Lipschitz continuity of the approximate solution mapping for parametric set-valued vector equilibrium problems is established by using a scalarization method. As applications of these results, the Lipschitz continuity of approximate solution mapping for parametric set-valued vector optimization problem is studied, and sufficient conditions of the Lipschitz continuity of approximate solution mapping for parametric set-valued vector optimization problem are gained.
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