Connectedness of Approximate Solution Sets to Parametric Generalized Vector Equilibrium Problems
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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.Abstract: 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.
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[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] GPFERT 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))
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