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

向量拟平衡问题系统及其应用

彭建文 杨新民 朱道立

彭建文, 杨新民, 朱道立. 向量拟平衡问题系统及其应用[J]. 应用数学和力学, 2006, 27(8): 963-970.
引用本文: 彭建文, 杨新民, 朱道立. 向量拟平衡问题系统及其应用[J]. 应用数学和力学, 2006, 27(8): 963-970.
PENG Jian-wen, YANG Xin-min, ZHU Dao-li. System of Vector Quasi-Equilibrium Problems and Its Applications[J]. Applied Mathematics and Mechanics, 2006, 27(8): 963-970.
Citation: PENG Jian-wen, YANG Xin-min, ZHU Dao-li. System of Vector Quasi-Equilibrium Problems and Its Applications[J]. Applied Mathematics and Mechanics, 2006, 27(8): 963-970.

向量拟平衡问题系统及其应用

基金项目: 国家自然科学基金资助项目(10171118;70432001);重庆市教委应用基础研究基金资助项目(030801);重庆市自然科学基金资助项目(8409);中国博士后基金资助项目
详细信息
    作者简介:

    彭建文(1967- ),男,四川仁寿人,副教授,博士(联系人.Tel:+86-23-65362798;E-mail:jwpeng6@yahoo.com.cn).

  • 中图分类号: O255;O177.92

System of Vector Quasi-Equilibrium Problems and Its Applications

  • 摘要: 引入了向量拟平衡问题系统并证明了其解的存在性定理.作为应用,还得到约束多目标对策和无约束多目标对策弱Pareto平衡的一些存在性结果.
  • [1] Ionescu Tulcea C.On the approximation of upper semi-continuous correspondences and the equilibriums of generalized games[J].J Math Anal Appl,1988,136(1):267—289. doi: 10.1016/0022-247X(88)90130-8
    [2] Yuan G X-Z,Isac G,Lai K K,et al.The study of minimax inequlities, abstract economics and applications to variational inequalities and Nash equilibria[J].Acta Appl Math,1998,54(1):135—166. doi: 10.1023/A:1006095413166
    [3] Ansari Q H,Schaible S, Yao J C.Systems of vector equilibrium problems and its applications[J].J Optim Theory Appl,2000,107(3):547—557. doi: 10.1023/A:1026495115191
    [4] 陈光亚,于辉.随机平衡系统解的存在性[J].系统科学与数学, 2002,[STHZ]. 22[STBZ]. (3):278—284.
    [5] Zhou J X, Chen G.Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities[J].J Math Anal Appl,1988,132(1):213—225. doi: 10.1016/0022-247X(88)90054-6
    [6] 张石生.变分不等式和相补问题理论及应用[M].上海:上海科学技术文献出版社,1991.
    [7] Shafer W,Sonnenschein H.Equilibrium in abstract economies without ordered preferences[J].J Math Econom,1975,2(2):345—348. doi: 10.1016/0304-4068(75)90002-6
    [8] 潘吉勋,张顺明.经济均衡的数学原理[M].长春:吉林大学出版社,1997.
    [9] Debreu G.A social equilibrium existence theorem[J].Proc Nat Acad Sci USA,1952,38(2):386—393.
    [10] Ding X P.Quasi-equilibrium problems with applications to infinite optimization and constrained games in general topological spaces[J].Appl Math Lett,2000,13(1):21—26.
    [11] Nash J F.Noncooperative games[J].Ann Math,1951,54(1):286—295. doi: 10.2307/1969529
    [12] Wang S Y.Existence of a Pareto equilibrium[J].J Optim Theory Appl, 1993,79(2):373—384. doi: 10.1007/BF00940586
    [13] Wang S Y.An existence theorem of a Pareto equilibrium[J].Appl Math Lett,1991,4(1):61—63.
    [14] Yu J,Yuan G X-Z.The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods[J].Comput Math Appl,1998,35(9):17—24.
    [15] Yuan X Z, Tarafdar E. Non-compact Pareto equilibria for multiobjective games[J]. J Math Anal Appl,1996,204(1):156—163. doi: 10.1006/jmaa.1996.0429
    [16] Luc D T.Theory of Vector Optimization[M].Berlin:Springer-Verlag,1989.
    [17] Luc D T,Vargas C A.A saddle-point theorem for set-valued maps[J].Nonlinear Analysis:Theory, Methods, and Applications,1992,18(1):1—7. doi: 10.1016/0362-546X(92)90044-F
    [18] Tanaka T.Generalized semicontinuity and existence theorems for cone saddle points[J].Appl Math Optim,1997,36(3):313—322. doi: 10.1007/s002459900065
    [19] Nash J F.Equilibrium point in n-person games[J].Proc Nat Acad Sci USA,1950,36(1):48—49. doi: 10.1073/pnas.36.1.48
    [20] Tian G Q,Zhou J X.Quasi-variational inequalities without the concavity assumption[J].J Math Anal Appl,1993,172(1):289—299. doi: 10.1006/jmaa.1993.1025
    [21] Kelley J, Namioka I.Linear Topological Space[M].New York/Heidelberg/Berlin:Springer,1963.
    [22] Michael E.A note on paracompact spaces[J].Proc Amer Math Soc,1953,4(5):831—838. doi: 10.1090/S0002-9939-1953-0056905-8
    [23] Fan K.Fixed-point and minimax theorems in locally convex topological linear spaces[J].Proc Nat Acad Sci USA,1952,38(1):121—126. doi: 10.1073/pnas.38.2.121
    [24] Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons,1984.
  • 加载中
计量
  • 文章访问数:  2673
  • HTML全文浏览量:  125
  • PDF下载量:  604
  • 被引次数: 0
出版历程
  • 收稿日期:  2003-06-27
  • 修回日期:  2005-12-02
  • 刊出日期:  2006-08-15

目录

    /

    返回文章
    返回