Smooth and nonsmooth analyses of vector-valued functions associated with circular cones

Yu Lin Chang*, Ching Yu Yang, 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

14 引文 斯高帕斯(Scopus)

摘要

Let Lθ be the circular cone in Rn which includes a second-order cone as a special case. For any function f from R to R, one can define a corresponding vector-valued function fc(x) on Rn by applying f to the spectral values of the spectral decomposition of x ⋯ Rn with respect to . We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as semismoothness. These results will play a crucial role in designing solution methods for optimization problem associated with the circular cone.

原文英語
頁(從 - 到)160-173
頁數14
期刊Nonlinear Analysis, Theory, Methods and Applications
85
DOIs
出版狀態已發佈 - 2013

ASJC Scopus subject areas

  • 分析
  • 應用數學

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