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On the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space

Xin-He Miao Jein-Shan Chen

Optimization and Control mathscidoc:1910.43956

Numerical functional analysis and optimization, 32, (5), 507-523, 2011.4
In this article, we consider the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. We establish several results that are standard and important when dealing with complementarity problems. These include proving the same growth of the FishcherBurmeister merit function and the natural residual merit function, investigating property of bounded level sets under mild conditions via different merit functions, and providing global error bounds through the proposed merit functions. Such results are helpful for further designing solution methods for the Lorentz cone complementarity problems in Hilbert space.
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@inproceedings{xin-he2011on,
  title={On the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space},
  author={Xin-He Miao, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020230039845549485},
  booktitle={Numerical functional analysis and optimization},
  volume={32},
  number={5},
  pages={507-523},
  year={2011},
}
Xin-He Miao, and Jein-Shan Chen. On the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. 2011. Vol. 32. In Numerical functional analysis and optimization. pp.507-523. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020230039845549485.
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