The penalized Fischer-Burmeister SOC complementarity function

Authors:
Shaohua Pan;Jein-Shan Chen;Sangho Kum;Yongdo Lim
Affiliations:
School of Mathematical Sciences, South China University of Technology, Guangzhou, China 510640;Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677;Department of Mathematics Education, Chungbuk National University, Cheongju, Korea 361-763;Department of Mathematics, Kyungpook National University, Taegu, Korea 702-701
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

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 R 01-property, although it is not continuously differentiable. Numerical results are included to illustrate the theoretical considerations.