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

Yu-Lin Chang Ching-Yu Yang Jein-Shan Chen

Optimization and Control mathscidoc:1910.43895

Nonlinear Analysis: Theory, Methods & Applications, 85, 160-173, 2013.7
Let L be the circular cone in R n 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 f c (x) on R n by applying f to the spectral values of the spectral decomposition of x R n with respect to L . We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Frchet 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.
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@inproceedings{yu-lin2013smooth,
  title={Smooth and nonsmooth analyses of vector-valued functions associated with circular cones},
  author={Yu-Lin Chang, Ching-Yu Yang, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223956895248424},
  booktitle={Nonlinear Analysis: Theory, Methods & Applications},
  volume={85},
  pages={160-173},
  year={2013},
}
Yu-Lin Chang, Ching-Yu Yang, and Jein-Shan Chen. Smooth and nonsmooth analyses of vector-valued functions associated with circular cones. 2013. Vol. 85. In Nonlinear Analysis: Theory, Methods & Applications. pp.160-173. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223956895248424.
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