The penalized Fischer-Burmeister SOC complementarity function

Shaohua Pan Jein-Shan Chen Sangho Kum Yongdo Lim

Optimization and Control mathscidoc:1910.43933

Computational Optimization and Applications, 49, (3), 457-491, 2011.7
In this paper, we study the properties of the penalized Fischer-Burmeister (FB) second-order cone (SOC) complementarity function. We show that the function possesses similar desirable properties of the FB SOC complementarity function for local convergence; for example, with the function the second-order cone complementarity problem (SOCCP) can be reformulated as a (strongly) semismooth system of equations, and the corresponding nonsmooth Newton method has local quadratic convergence without strict complementarity of solutions. In addition, the penalized FB merit function has bounded level sets under a rather weak condition which can be satisfied by strictly feasible monotone SOCCPs or SOCCPs with the Cartesian <i>R</i> <sub>01</sub>-property, although it is not continuously differentiable. Numerical results are included to illustrate the theoretical considerations.
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  title={The penalized Fischer-Burmeister SOC complementarity function},
  author={Shaohua Pan, Jein-Shan Chen, Sangho Kum, and Yongdo Lim},
  booktitle={Computational Optimization and Applications},
Shaohua Pan, Jein-Shan Chen, Sangho Kum, and Yongdo Lim. The penalized Fischer-Burmeister SOC complementarity function. 2011. Vol. 49. In Computational Optimization and Applications. pp.457-491.
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