The same growth of FB and NR symmetric cone complementarity functions

Shujun Bi, Shaohua Pan, Jein Shan Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We establish that the Fischer-Burmeister (FB) complementarity function and the natural residual (NR) complementarity function associated with the symmetric cone have the same growth, in terms of the classification of Euclidean Jordan algebras. This, on the one hand, provides an affirmative answer to the second open question proposed by Tseng (J Optim Theory Appl 89:17-37, 1996) for the matrix-valued FB and NR complementarity functions, and on the other hand, extends the third important inequality of Lemma 3. 1 in the aforementioned paper to the setting of Euclidean Jordan algebras. It is worthwhile to point out that the proof is surprisingly simple.

Original languageEnglish
Pages (from-to)153-162
Number of pages10
JournalOptimization Letters
Issue number1
Publication statusPublished - 2012 Jan


  • FB and NR complementarity functions
  • Growth
  • Symmetric cone

ASJC Scopus subject areas

  • Control and Optimization


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