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Two classes of merit functions for infinite-dimensional second order complimentary problems

Juhe Sun Jein-Shan Chen

Optimization and Control mathscidoc:1910.43944

Numerical functional analysis and optimization, 31, (4), 387-413, 2010.6
In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.
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@inproceedings{juhe2010two,
  title={Two classes of merit functions for infinite-dimensional second order complimentary problems},
  author={Juhe Sun, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225717195809473},
  booktitle={Numerical functional analysis and optimization},
  volume={31},
  number={4},
  pages={387-413},
  year={2010},
}
Juhe Sun, and Jein-Shan Chen. Two classes of merit functions for infinite-dimensional second order complimentary problems. 2010. Vol. 31. In Numerical functional analysis and optimization. pp.387-413. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225717195809473.
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