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Computational Optimization and Applications

, Volume 49, Issue 3, pp 457–491 | Cite as

The penalized Fischer-Burmeister SOC complementarity function

  • Shaohua Pan
  • Jein-Shan Chen
  • Sangho Kum
  • Yongdo Lim
Article

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.

Second-order cone complementarity problem Penalized Fischer-Burmeister function Nonsmooth Newton method B-subdifferential Coerciveness 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Shaohua Pan
    • 1
  • Jein-Shan Chen
    • 2
  • Sangho Kum
    • 3
  • Yongdo Lim
    • 4
  1. 1.School of Mathematical SciencesSouth China University of TechnologyGuangzhouChina
  2. 2.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan
  3. 3.Department of Mathematics EducationChungbuk National UniversityCheongjuKorea
  4. 4.Department of MathematicsKyungpook National UniversityTaeguKorea

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