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

Connectedness of Approximate Solution Sets to Parametric Generalized Vector Equilibrium Problems

doi: 10.21656/1000-0887.380279
Funds:  The National Natural Science Foundation of China(11401487)
  • Received Date: 2017-11-01
  • Rev Recd Date: 2018-01-11
  • Publish Date: 2018-10-01
  • Several approximate solution sets to generalized vector equilibrium problems were studied. The scalarization characterization of ε-approximate solutions to parametric generalized vector equilibrium problems was established by means of the C-subconvexlike property of the involved mappings. Further, the connectedness of the 2 types of approximate solution sets was derived with the scalarization methods. Finally, the relationships among these approximate solution sets were obtained under some typical conditions.
  • loading
  • [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

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1277) PDF downloads(553) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return