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On the existence of saddle points for nonlinear second-order cone programming problems

Jinchuan Zhou Jein-Shan Chen

Optimization and Control mathscidoc:1910.43939

Journal of Global Optimization, 62, (3), 459-480, 2015.7
In this paper, we study the existence of local and global saddle points for nonlinear second-order cone programming problems. The existence of local saddle points is developed by using the second-order sufficient conditions, in which a sigma-term is added to reflect the curvature of second-order cone. Furthermore, by dealing with the perturbation of the primal problem, we establish the existence of global saddle points, which can be applicable for the case of multiple optimal solutions. The close relationship between global saddle points and exact penalty representations are discussed as well.
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@inproceedings{jinchuan2015on,
  title={On the existence of saddle points for nonlinear second-order cone programming problems},
  author={Jinchuan Zhou, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225452466107468},
  booktitle={Journal of Global Optimization},
  volume={62},
  number={3},
  pages={459-480},
  year={2015},
}
Jinchuan Zhou, and Jein-Shan Chen. On the existence of saddle points for nonlinear second-order cone programming problems. 2015. Vol. 62. In Journal of Global Optimization. pp.459-480. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225452466107468.
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