Conditions for error bounds and bounded level sets of some merit functions for the second-order cone complementarity problem

Jein-Shan Chen

Optimization and Control mathscidoc:1910.43896

Journal of Optimization Theory and Applications, 135, (3), 459-473, 2007.12
Recently this author studied several merit functions systematically for the second-order cone complementarity problem. These merit functions were shown to enjoy some favorable properties, to provide error bounds under the condition of strong monotonicity, and to have bounded level sets under the conditions of monotonicity as well as strict feasibility. In this paper, we weaken the condition of strong monotonicity to the so-called uniform <i>P</i> <sup>*</sup>-property, which is a new concept recently developed for linear and nonlinear transformations on Euclidean Jordan algebra. Moreover, we replace the monotonicity and strict feasibility by the so-called <i>R</i> <sub>01</sub> or <i>R</i> <sub>02</sub>-functions to keep the property of bounded level sets.
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@inproceedings{jein-shan2007conditions,
  title={Conditions for error bounds and bounded level sets of some merit functions for the second-order cone complementarity problem},
  author={Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224015047981425},
  booktitle={Journal of Optimization Theory and Applications},
  volume={135},
  number={3},
  pages={459-473},
  year={2007},
}
Jein-Shan Chen. Conditions for error bounds and bounded level sets of some merit functions for the second-order cone complementarity problem. 2007. Vol. 135. In Journal of Optimization Theory and Applications. pp.459-473. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224015047981425.
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