Banach空间上多值映射的度量次正则性
发布时间：2018-09-12 06:13
【摘要】：这篇文章主要讨论Banach空间上多值映射的度量次正则性Ioffe [Trans. Amer. Math. Soc.,251(1979), pp.61-69.]在局部Lipschitz实值函数的特殊情况下通过次微分映射给出了度量次正则性的充分条件Zheng与Ng[SIAM J. Optim.,20(2010), pp.2119-2136.]将Ioffe的结果推广到一般的多值映射.随后,Zheng和He [Nonlinear Anal.,100(2014), pp.116-127]又改进了Zheng与Ng的结果.本文又进一步改进了Zheng和He的结果,而且在Asplund空间和Frechet光滑的Banach空间的情况下得到更好的充分性条件.
[Abstract]:In this paper, we mainly discuss the metric subregularity Ioffe [Trans.] of multivalued mappings on Banach spaces. Amer. Math. Soc.,251 (1979), pp.61-69.] In the special case of local Lipschitz real value function, the sufficient conditions for metric subregularity of Zheng and Ng [SIAM J. Optim.,20 (2010), pp.2119-2136.] are given by subdifferential mapping. The results of Ioffe are generalized to general multivalued mappings. Then Zheng and He [Nonlinear Anal.,100 (2014), pp.116-127] improved the results of Zheng and Ng. In this paper, we further improve the results of Zheng and He, and obtain better sufficient conditions in the case of Asplund space and Frechet smooth Banach space.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177.2
本文编号：2238145
[Abstract]:In this paper, we mainly discuss the metric subregularity Ioffe [Trans.] of multivalued mappings on Banach spaces. Amer. Math. Soc.,251 (1979), pp.61-69.] In the special case of local Lipschitz real value function, the sufficient conditions for metric subregularity of Zheng and Ng [SIAM J. Optim.,20 (2010), pp.2119-2136.] are given by subdifferential mapping. The results of Ioffe are generalized to general multivalued mappings. Then Zheng and He [Nonlinear Anal.,100 (2014), pp.116-127] improved the results of Zheng and Ng. In this paper, we further improve the results of Zheng and He, and obtain better sufficient conditions in the case of Asplund space and Frechet smooth Banach space.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177.2
【参考文献】
相关期刊论文 前1条
1 刘新宇;;C++ Lite Memo[J];程序员;2009年04期
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