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含参弱向量均衡问题的适定性 被引量：1

Well-posedness for Parametric Weak Vector Equilibrium Problems
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摘要 在实Hausdorff拓扑线性空间中研究了含参弱向量均衡问题的适定性.证明了在适当条件下由近似网定义的含参适定性等价于近似解映射的上半连续性,并给出了所研究问题各种适定的充分性条件. It studied the well-posedness for parametric weak vector equilibrium problems in real Hausdorff topological vector spaces.It prooved that under suitable conditions the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution mapping and gave sufficient conditions to various kinds of well-posedness.
作者 马博厂 龚循华
机构地区 南昌大学数学系
出处 《应用泛函分析学报》 CSCD 2011年第2期172-179,共8页 Acta Analysis Functionalis Applicata
基金 国家自然科学基金(11061023) 江西自然科学基金(2008GZS0072) 江西省研究生创新专项资金自筹项目(YC09B004)
关键词 含参弱向量均衡问题 适定性 解映射 上半连续性 parametric weak vector equilibrium problems well-posedness solution mapping upper semicontinuity
分类号 O317 [理学—一般力学与力学基础]
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参考文献12

  • 1Dontchev A L, Zolezzi. Well-posed Optimization Problems[M]. Berlin: Heidelberg, 1993.
  • 2Chen G Y, Huang X X, Ya,ng X Q. Vector Optimization: Set-valued and Variational Analysis[M]. Berlin: Heidelberg, 2005.
  • 3Lemaire B, Salem C O A, Revalski. Well-posedness by peturbations of variational problems[J]. J Optim Theory Appl, 2002, 215: 345-368.
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同被引文献12

  • 1Tikhonov A N. On the stability of the functional optimization problem[J]. USSR Computational Mathematics and Mathematical Physics, 1966, 6(4): 28-33.
  • 2Levitin E S, Polyak B T. Convergence of minimizing sequences in conditional extremum prob- lems[J]. Doklady Akademii Nauk SSSR, 1966, 168(5): 997-8.
  • 3Yang H, Yu J. Unified approaches to well-posedness with some applications[J]. Journal of Global Optimization, 2005, 31(3): 371-381.
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  • 5Ceng L C, Hadjisavvas N, Schaible S, Yao J C.Well-posedness for mixed quasivariational-like inequalities[J]. Journal of Optimization Theory and Applications, 2008, 139(1): 109-125.
  • 6Li M H, Li S J, Zhang W Y. Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems[J]. Journal of Industrial and Management Optimization, 2009, 5(4): 683-696.
  • 7Long X J, Huang N J. Metric characterizations of a-well-posedness for symmetric quasi-equilibrium problems[J]. Journal of Global Optimization, 2009, 45(3): 459-471.
  • 8Kimura K, Liou Y, Wu S, Yao, J C. Well-posedness for parametric vector equilibrium problems with applications[J]. Journal of Industrial and Management Optimization, 2008, 4(2): 313-327.
  • 9Anh L Q, Khanh P Q, VanD TM, Yao J C. Wetl-posedness for vector quasiequilibria[J]. Talwanese Journal of Mathematics, 2009, 13(2B): 713-737.
  • 10Li Q Y, Wang S H. Well-posedness for parametric strong vector quasi-equilibrium problems with applications[J]; Fixed Point Theory and Applications, 2011(1): 1-14.

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应用泛函分析学报
2011年 第2期

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