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参数广义弱向量拟平衡问题解映射的H-连续性刻画

邵重阳 彭再云 王泾晶 周大琼

邵重阳, 彭再云, 王泾晶, 周大琼. 参数广义弱向量拟平衡问题解映射的H-连续性刻画[J]. 应用数学和力学, 2019, 40(4): 452-462. doi: 10.21656/1000-0887.390198
引用本文: 邵重阳, 彭再云, 王泾晶, 周大琼. 参数广义弱向量拟平衡问题解映射的H-连续性刻画[J]. 应用数学和力学, 2019, 40(4): 452-462. doi: 10.21656/1000-0887.390198
SHAO Chongyang, PENG Zaiyun, WANG Jingjing, ZHOU Daqiong. Characterizations of HContinuity for Solution Mapping to Parametric Generalized Weak Vector QuasiEquilibrium Problems[J]. Applied Mathematics and Mechanics, 2019, 40(4): 452-462. doi: 10.21656/1000-0887.390198
Citation: SHAO Chongyang, PENG Zaiyun, WANG Jingjing, ZHOU Daqiong. Characterizations of HContinuity for Solution Mapping to Parametric Generalized Weak Vector QuasiEquilibrium Problems[J]. Applied Mathematics and Mechanics, 2019, 40(4): 452-462. doi: 10.21656/1000-0887.390198

参数广义弱向量拟平衡问题解映射的H-连续性刻画

doi: 10.21656/1000-0887.390198
基金项目: 国家自然科学基金(11431004;11471059);重庆市自然科学基金(cstc2017jcyjAX0382;cstc2018jcyjAX0337);重庆市创新团队(CXTDX201601022);重庆市巴渝学者计划
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

Characterizations of HContinuity for Solution Mapping to Parametric Generalized Weak Vector QuasiEquilibrium Problems

Funds: The National Natural Science Foundation of China(11431004;11471059)
  • 摘要: 研究了Hausdorff拓扑向量空间中的一类参数广义弱向量拟平衡问题(PGWVQEP)的稳定性.首先,给出了此问题的参数间隙函数,研究了参数间隙函数的连续性.然后, 提出了一个与参数间隙函数相关的关键假设,讨论了它的连续性,并给出关键假设的等价刻画.最后, 借助于假设,获得了PGWVQEP解映射Hausdorff半连续的充分必要条件.并举例验证了所得结果.
  • [1] BLUM E, OETTLI W. From optimization and variational inequalities to equilibrium problems[J]. The Mathmatics Student,1994,63: 123-145.
    [2] BIANCHI M, HADJISAVVAS N, SCHAIBLE S. Vector equilibrium problems with generalized monotone bifunctions[J].Journal of Optimization Theory and Applications,1997,92(3): 527-542.
    [3] ANSARI Q H, OETTLI W, SCHLAGER D. A generalization of vectorial equilibria[J]. Mathematical Methods of Operations Research,1997,46(2): 147-152.
    [4] 〖JP2〗LONG X J, HUANG N J, TEO K L. Existence and stability of solutions for generalized strong vector quasi-equilibrium problem[J]. Mathematical and Computer Modelling,2008,47(3/4): 445-451.
    [5] GONG X H. Continuity of the solution set to parametric weak vector equilibrium problems[J]. Journal of Optimization Theory and Applications,2008,139(1): 35-46.
    [6] GONG X H, YAO J C. Lower semicontinuity of the set of efficient solutions for generalized systems[J]. Journal of Optimization Theory and Applications,2008,138(2): 197-205.
    [7] ANH L Q, KHANH P Q. Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks ii: lower semicontinuities applications[J]. Set-Valued Analysis,2008,16(7/8): 943-960.
    [8] ANH L Q, KHANH P Q. Continuity of solution maps of parametric quasiequilibrium problems[J]. Journal of Global Optimization,2010,46(2): 247-259.
    [9] KIMURA K, YAO J C. Semicontinuity of solution mappings of parametric generalized vector equilibrium problems[J]. Journal of Optimization Theory and Applications,2008,138(3): 429-443.
    [10] KIMURA K, YAO J C. Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems[J]. Journal of Global Optimization,2008,41(2): 187-202.
    [11] 曾静, 彭再云, 张石生. 广义强向量拟平衡问题解的存在性和Hadamard适定性[J]. 应用数学和力学, 2015,36(6): 651-658.(ZENG Jing, PENG Zaiyun, ZHANG Shisheng. Existence and Hadamard well-posedness of solutions to generalized strong vector quasi-equilibrium problems[J]. Applied Mathematics and Mechanics,2015,36(6): 651-658.(in Chinese))
    [12] PENG Z Y, PENG J W, LONG X J, et al. On the stability of solutions for semi-infinite vector optimization problems[J]. Journal of Global Optimization,2018,70(1): 55-69.
    [13] PENG Z Y, WANG X F, YANG X M. Connectedness of approximate efficient solutions for generalized semi-infinite vector optimization problems[J]. Set-Valued and Variational Analysis,2019,27(1): 103-118.
    [14] LI S J, CHEN C R. Stability of weak vector variational inequality[J]. Nonlinear Analysis: Theory, Methods & Applications,2009,70(4): 1528-1535.
    [15] CHEN C R, LI S J. Semicontinuity of the solution set map to a set-valued weak vector variational inequality[J]. Journal of Industrial and Management Optimization,2007,3(3): 519-528.
    [16] CHEN C R, LI S J, FANG Z M. On the solution semicontinuity to a parametric generalized vector quasi- variational inequality[J]. Computers & Mathematics With Applications,2010,60(8): 2417-2425.
    [17] ZHONG R Y, HUANG N J. Lower semicontinuity for parametric weak vector variational inequalities in reflexive Banach spaces[J]. Journal of Optimization Theory and Applications,2011,149(3): 564-579.
    [18] ANH L Q, HUNG N V. Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems[J]. Journal of Industrial & Management Optimization,2018,14(1): 65-79.
    [19] ZHONG R Y, HUANG N J. On the stability of solution mapping for parametric generalized vector quasiequilibrium problems[J]. Computers & Mathematics With Applications,2012,63(4): 807-815.
    [20] AUBIN J P, EKELAND I. Applied Nonlinear Analysis [M]. New York: John Wiley and Sons, 1984.
    [21] BERGE C. Topological Spaces [M]. London: Oliver and Boyd, 1963.
    [22] Gerstewitz C. Nichtkonvexe dualitat in der vektaroptimierung[J]. Wissenschafliche Zeitschift der Technischen Hochschule Leuna-Mensehung,1983,25: 357-364.
    [23] LUC D T. Theory of Vector Optimization, Lecture Notes in Economic and Mathematical Systems [M]. Berlin: Springer-Verlag, 1989.
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出版历程
  • 收稿日期:  2018-07-17
  • 修回日期:  2018-08-31
  • 刊出日期:  2019-04-01

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