A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems

Yasushi Narushima, Nobuko Sagara, Hideho Ogasawara

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17 Citations (Scopus)


The second-order cone complementarity problem (SOCCP) is an important class of problems containing a lot of optimization problems. The SOCCP can be transformed into a system of nonsmooth equations. To solve this nonsmooth system, smoothing techniques are often used. Fukushima, Luo and Tseng (SIAM J. Optim. 12:436-460, 2001) studied concrete theories and properties of smoothing functions for the SOCCP. Recently, a practical computational method using the smoothed natural residual function to solve the SOCCP was given by Chen, Sun and Sun (Comput. Optim. Appl. 25:39-56, 2003). In the present paper, we propose an algorithm to solve the SOCCP by using the smoothed Fischer-Burmeister function. Some preliminary numerical results are given.

Original languageEnglish
Pages (from-to)79-101
Number of pages23
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1 Feb 2011



  • Fischer-Burmeister function
  • Global convergence
  • Second-order cone complementarity problem
  • Smoothing method
  • Superlinear convergence

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