留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

含参广义向量均衡问题近似解集的连通性

巨兴兴 陈加伟 张俊容 李高西

巨兴兴, 陈加伟, 张俊容, 李高西. 含参广义向量均衡问题近似解集的连通性[J]. 应用数学和力学, 2018, 39(10): 1206-1212. doi: 10.21656/1000-0887.380279
引用本文: 巨兴兴, 陈加伟, 张俊容, 李高西. 含参广义向量均衡问题近似解集的连通性[J]. 应用数学和力学, 2018, 39(10): 1206-1212. doi: 10.21656/1000-0887.380279
JU Xingxing, CHEN Jiawei, ZHANG Junrong, LI Gaoxi. Connectedness of Approximate Solution Sets to Parametric Generalized Vector Equilibrium Problems[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1206-1212. doi: 10.21656/1000-0887.380279
Citation: JU Xingxing, CHEN Jiawei, ZHANG Junrong, LI Gaoxi. Connectedness of Approximate Solution Sets to Parametric Generalized Vector Equilibrium Problems[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1206-1212. doi: 10.21656/1000-0887.380279

含参广义向量均衡问题近似解集的连通性

doi: 10.21656/1000-0887.380279
基金项目: 国家自然科学基金(11401487);重庆市基础与前沿研究计划项目(cstc2016jcyjA0239)
详细信息
    作者简介:

    巨兴兴(1993—),男,硕士生(E-mail: juxxmath@163.com);陈加伟(1984—),男,副教授,博士(通讯作者. E-mail: J.W.Chen713@163.com).

  • 中图分类号: O357.41

Connectedness of Approximate Solution Sets to Parametric Generalized Vector Equilibrium Problems

Funds: The National Natural Science Foundation of China(11401487)
  • 摘要: 主要研究了含参广义向量均衡问题的几类近似解.在C次似凸性的条件下, 建立了该类含参广义向量均衡问题ε-弱近似解的标量化特征, 并得到该类含参广义向量均衡问题两类近似解集的连通性.通过举例说明了所得结果的正确性.
  • [1] LUC D T. Connectedness of the efficient point sets in quasiconcave vector maximization[J]. Journal of Mathematical Analysis and Applications,1987,122(2): 346-354.
    [2] GONG X H. Connectedness of efficient solution sets for set-valued maps in normed spaces[J]. Journal of Optimization Theory and Applications,1994,83(1): 83-96.
    [3] CHEN B, LIU Q Y, LIU Z B, et al. Connectedness of approximate solutions set for vector equilibrium problems in Hausdorff topological vector spaces[J]. Fixed Point Theory and Applications,2011,2011(1): 1-11.
    [4] HAN Y, HUANG N J. Some characterizations of the approximate solutions to generalized vector equilibrium problems[J]. Journal of Industrial and Management Optimization,2016,12(3): 1135-1151.
    [5] PENG Z Y, ZHAO Y, YANG X M. Semicontinuity of approximate solution mappings to parametric set-valued weak vector equilibrium problems[J]. Numerical Functional Analysis and Optimization,2015,36(4): 481-500.
    [6] LI X B, LI S J. Continuity of approximate solution mappings for parametric equilibrium problems[J]. Journal of Global Optimization,2011,51(3): 541-548.
    [7] WANG Q L, LI S J. Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem[J]. Journal of Industrial and Management Optimization,2014,10(4): 1225-1234.
    [8] SADEQI I, PAYDAR M S. Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems[J]. Optimization,2016,65(5): 1003-1021.
    [9] 韩瑜, 黄南京. 含参广义向量均衡问题有效解的稳定性[J]. 中国科学: 数学, 2017,47(3): 397-408.(HAN Yu, HUANG Nanjing. Stability of efficient solutions to parametric generalized vector equilibrium problems[J]. Scientia Sinica: Mathematica,2017,47(3): 397-408.(in Chinese))
    [10] GONG X H. Efficiency and henig efficiency for vector equilibrium problems[J]. Journal of Optimization Theory and Applications,2001,108(1): 139-154.
    [11] GPFERT A, RIAHI H, TAMMER C, et al. Variational Methods in Partially Ordered Spaces [M]. New York: Springer, 2003.
    [12] LI Z F, CHEN G Y. Lagrangian multipliers, saddle points, and duality in vector optimization of set-valued maps[J]. Journal of Mathematical Analysis and Applications,1997,215(2): 297-316.
    [13] 杨丽, 李军. Hilbert空间中分裂可行性问题的改进Halpern迭代和黏性逼近算法[J]. 应用数学和力学, 2017,38(9): 1072-1080.(YANG Li, LI Jun. Modified Halpern iteration and viscosity approximation methods for the split feasibility problems in Hilbert spaces[J]. Applied Mathematics and Mechanics,2017,〖STHZ〗 38(9): 1072-1080.(in Chinese))
    [14] 彭再云, 李科科, 张石生. 向量D-η-E-半预不变凸映射与向量优化[J]. 应用数学和力学, 2014,35(9): 1020-1032.(PENG Zaiyun, LI Keke, ZHANG Shisheng. D-η-E-semipreinvex vector mapping and vector optimization[J]. Applied Mathematics and Mechanics,2014,35(9): 1020-1032.(in Chinese))
    [15] 赵勇, 彭再云, 张石生. 向量优化问题有效点集的稳定性[J]. 应用数学和力学, 2013,34(6): 643-650.(ZHAO Yong, PENG Zaiyun, ZHANG Shisheng. Stability of the sets of effective points of vector-valued optimization problems[J]. Applied Mathematics and Mechanics,2013,34(6): 643-650.(in Chinese))
  • 加载中
计量
  • 文章访问数:  1081
  • HTML全文浏览量:  143
  • PDF下载量:  553
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-11-01
  • 修回日期:  2018-01-11
  • 刊出日期:  2018-10-01

目录

    /

    返回文章
    返回