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基于改进集的带约束集值向量均衡问题的最优性条件

陈望 周志昂

陈望, 周志昂. 基于改进集的带约束集值向量均衡问题的最优性条件[J]. 应用数学和力学, 2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104
引用本文: 陈望, 周志昂. 基于改进集的带约束集值向量均衡问题的最优性条件[J]. 应用数学和力学, 2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104
CHEN Wang, ZHOU Zhiang. Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104
Citation: CHEN Wang, ZHOU Zhiang. Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104

基于改进集的带约束集值向量均衡问题的最优性条件

doi: 10.21656/1000-0887.390104
基金项目: 国家自然科学基金(11431004;11471291);重庆市前沿与应用基础研究计划项目(cstc2015jcyjA00050;cstc2017jcyjBX0055;cstc2015jcyjBX0113)
详细信息
    作者简介:

    陈望(1994—),男,硕士生(E-mail: wf835518304@163.com);周志昂(1972—),男,教授,博士(通讯作者. E-mail: zhi_ang@163.com).

  • 中图分类号: O221.6

Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets

Funds: The National Natural Science Foundation of China(11431004;11471291)
  • 摘要: 在局部凸空间中,研究了带约束集值向量均衡问题的最优性条件.首先,利用改进集引进了带约束集值向量均衡问题的E-Henig真有效解和E-超有效解的概念.其次,在邻近E-次似凸的假设下,建立了带约束集值向量均衡问题的E-Henig真有效解的充分必要性条件.最后,在邻近E-次似凸的假设下,建立了带约束集值向量均衡问题的E-超有效解的必要性条件.
  • [1] 龚循华, 乐华明. 向量均衡问题有效解与强解的存在性[J]. 南昌大学学报(理科版), 2008,32(1): 1-5.(GONG Xunhua, YUE Huaming. Existence of efficient solutions and strong solutions for vector equilibrium problems[J]. Journal of Nanchang University(Natural Science),2008,32(1): 1-5.(in Chinese))
    [2] CAPT A. Existence results for proper efficient solutions of vector equilibrium problems and applications[J]. Journal of Global Optimization,2011,51(4): 657-675.
    [3] GONG X H. Connectedness of the solution sets and scalarization for vector equilibrium problems[J]. Journal of Optimization Theory and Applications,2007,133(2): 151-161.
    [4] LONG X J, PENG J W. Connectedness and compactness of weak efficient solutions for vector equilibrium problems[J]. Bulletin of the Korean Mathematical Society,2011,48(6): 1225-1233.
    [5] GONG X H. Optimality conditions for vector equilibrium problems[J]. Journal of Mathematics Analysis and Applications,2008,342(2): 1455-1466.
    [6] 龚循华, 熊淑群. 类凸向量均衡问题解的最优性条件[J]. 南昌大学学报(理科版), 2009,33(5): 409-414.(GONG Xunhua, XIONG Shuqun. Optimality conditions for convex-like vector equilibrium problem[J]. Journal of Nanchang University(Natural Science),2009,33(5): 409-414.(in Chinese))
    [7] QIU Q S. Optimality conditions of globally efficient solution for vector equilibrium problems with generalized convexity[J]. Journal of Inequalities and Applications,2009,2009(1): 1-13.
    [8] MA C B, GONG X H. Optimality conditions for vector equilibrium problems in normed spaces[J]. Optimization,2011,60(12): 1441-1455.
    [9] ZHAO K Q, YANG X M, PENG J W. Weak E-optimal solution in vector optimization[J]. Taiwanese Journal of Mathematics,2013,17(4): 1287-1302.
    [10] ZHAO K Q, YANG X M. E -Benson proper efficiency in vector optimization[J]. Optimization,2015,64(4): 739-752.
    [11] ZHOU Z A, YANG X M, ZHAO K Q. E -super efficiency of set-valued optimization problems involving improvement sets[J]. Journal of Industrial and Management Optimization,2016,12(3): 1031-1039.
    [12] 唐莉萍, 杨玉红.E-Borwein真有效解的刻画[J]. 应用数学和力学, 2017,38(12): 1399-1404.(TANG Liping, YANG Yuhong. Characterizations of E-Borwein properly efficient solutions[J]. Applied Mathematics and Mechanics,2017,38(12): 1399-1404.(in Chinese))
    [13] CHEN C R, ZUO X, LU F, et al. Vector equilibrium problems under improvement sets and linear scalarization with stability applications[J]. Optimization Methods and Software,2016,31(6): 1240-1257.
    [14] 宋宁宁, 仇秋生. 基于改进集的向量均衡问题解的最优性条件[J]. 浙江师范大学学报(自然科学版), 2017,40(2): 130-136.(SONG Ningning, QIU Qiusheng. The optimality conditions of the vector equilibrium problems via improvement set[J]. Journal of Zhejiang Normal University(Nature Science),2017,40(2): 130-136.(in Chinese))
    [15] CHENG Y H, FU W T. Strong efficiency in a locally convex space[J]. Mathematical Methods of Operations Research,1999,50(3): 373-384.
    [16] GONG X H. Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior[J]. Journal of Mathematics Analysis and Applications,2005,307(1): 12-31.
    [17] GUTIERREZ C, JIMENEZ B, NOVO V. Improvement sets and vector optimization[J]. European Journal of Operational Research,2012,223(2): 304-311.
    [18] GONG X H, FU W T, LIU W. Super efficiency for a vector equilibrium in locally convex topological vector spaces[M]//Giannessi F, ed. Vector Variational Inequalities and Vector Equilibria . Nonconvex Optimization and Its Applications, Vol38. Boston, MA: Springer, 2000.
    [19] ZHENG X Y. Proper efficiency in locally convex topological vector spaces[J]. Journal of Optimization Theory and Applications,1997,94(2): 469-486.
    [20] 丘京辉, 张申媛. 严有效点与Henig真有效点[J]. 数学杂志, 2005,〖STHZ〗 25(2): 203-209.(QIU Jinghui, ZHANG Shenyuan. Strictly efficient points and Henig proper efficient points[J]. Journal of Mathematics,2005,25(2): 203-209.(in Chinese))
    [21] 傅万涛. 赋范线性空间集合的严有效点[J]. 系统科学与数学, 1997,17(4): 324-329.(FU Wantao. On strictly efficient point of a set in a normed linear space[J]. Journal of System Science and Mathematical Science Chinese Series,1997,17(4): 324-329.(in Chinese))
    [22] 仇秋生. 关于Henig真有效性[J]. 系统科学与数学, 2011,31(4): 482-488.(QIU Qiusheng. On Henig proper efficiency[J]. Journal of System Science and Mathematical Science Chinese Series,2011,31(4): 482-488.(in Chinese))
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出版历程
  • 收稿日期:  2018-04-02
  • 修回日期:  2018-04-09
  • 刊出日期:  2018-10-01

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