改进集映射下参数广义向量拟平衡问题解映射的Berge下半连续性

邵重阳; 彭再云; 刘芙萍; 王泾晶

doi:10.21656/1000-0887.400307

改进集映射下参数广义向量拟平衡问题解映射的Berge下半连续性

doi: 10.21656/1000-0887.400307

¹重庆交通大学数学与统计学院, 重庆 400074;²重庆师范大学数学科学学院, 重庆 400074

基金项目: 国家自然科学基金(11301571)；重庆市巴渝学者计划；重庆市基础与前沿研究项目(cstc2018jcyjAX0337)；重庆市创新团队(CXTDX201601022)；重庆市留学归国人员创新项目(cx2019148)

详细信息

作者简介:
邵重阳(1993—)，男，硕士(E-mail: shaocyll@sina.com)；彭再云(1980—)，男，教授，博士(通讯作者. E-mail: pengzaiyun@126.com).

中图分类号: O224
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- 文章访问数: 1217
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出版历程
- 收稿日期: 2019-10-14
- 修回日期: 2019-12-17
- 刊出日期: 2020-08-01

Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings

¹College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²School of Mathematical Sciences, Chongqing Normal University, Chongqing 400074, P.R.China

Funds: The National Natural Science Foundation of China(11301571)

摘要

摘要: 该文主要讨论了一类新的参数广义向量拟平衡问题解映射的稳定性.首先，定义了改进集映射，基于改进集映射，将序结构进行推广并应用于拟平衡问题的研究，得到了改进集映射下参数广义向量拟平衡问题(IPGVQEP).然后，给出了一类与改进集映射相关的非线性标量化函数Ψ，利用非线性标量化函数Ψ得到了与原问题(IPGVQEP)对应的标量化问题(IPGVQEP)_Ψ，并获得了原问题与标量化问题解之间的关系.最后，引入了一个关键假设H_Ψ，借助关键假设H_Ψ及原问题与标量化问题间解的关系，获得了IPGVQEP解映射Berge下半连续性的充分必要条件，并举例验证了所得结果.
- 改进集映射 /
- 参数广义向量拟平衡问题 /
- 解映射 /
- Berge下半连续性 /
- 标量化问题
Abstract: The Berge lower semi-continuity of solution mapping for a new class of parametric generalized vector quasi-equilibrium problems was discussed. Firstly, the improvement set mapping was defined, based on which the order structure was generalized and applied to the study of vector quasi-equilibrium problems, to lead to parametric generalized vector quasi-equilibrium problems under improvement set mappings (IPGVQEP). Then, a nonlinear scalarization function Ψ associated with the improvement set mapping was introduced, the scalar problem (IPGVQEP)_Ψ corresponding to the above problem (IPGVQEP) was given, and the relation between solution sets of (IPGVQEP) and (IPGVQEP)_Ψ was obtained. Finally, by virtue of a key hypothesis H_Ψ and the relation between solution sets, the sufficient and necessary conditions for Berge lower semi-continuity of the solution mapping for (IPGVQEP) were established, and an example was given to verify the results.
- improvement set mapping /
- parametric generalized vector quasi-equilibrium problem /
- solution mapping /
- Berge lower semi-continuity /
- scalarization problem

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参考文献(20)

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改进集映射下参数广义向量拟平衡问题解映射的Berge下半连续性

doi: 10.21656/1000-0887.400307

作者简介:
邵重阳(1993—)，男，硕士(E-mail: shaocyll@sina.com)；彭再云(1980—)，男，教授，博士(通讯作者. E-mail: pengzaiyun@126.com).

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Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings

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留言板

改进集映射下参数广义向量拟平衡问题解映射的Berge下半连续性

doi: 10.21656/1000-0887.400307

作者简介: 邵重阳(1993—)，男，硕士(E-mail: shaocyll@sina.com)；彭再云(1980—)，男，教授，博士(通讯作者. E-mail: pengzaiyun@126.com).

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出版历程

Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings

计量

出版历程

目录

作者简介:
邵重阳(1993—)，男，硕士(E-mail: shaocyll@sina.com)；彭再云(1980—)，男，教授，博士(通讯作者. E-mail: pengzaiyun@126.com).