Analysis of nonsmooth vector-valued functions associated with infinite-dimensional second-order cones

Ching Yu Yang, Yu Lin Chang, Jein Shan Chen*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

Given a Hilbert space H, the infinite-dimensional Lorentz/second-order cone K is introduced. For any x∈H, a spectral decomposition is introduced, and for any function f:R→R, we define a corresponding vector-valued function fH(x) on Hilbert space H by applying f to the spectral values of the spectral decomposition of x∈H with respect to K. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, differentiability, smoothness, as well as s-semismoothness. These results can be helpful for designing and analyzing solution methods for solving infinite-dimensional second-order cone programs and complementarity problems.

原文英語
頁(從 - 到)5766-5783
頁數18
期刊Nonlinear Analysis, Theory, Methods and Applications
74
發行號16
DOIs
出版狀態已發佈 - 2011 十一月

ASJC Scopus subject areas

  • 分析
  • 應用數學

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