| 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 |
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| 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) |
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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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