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The same growth of FB and NR symmetric cone complementarity functions

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Shujun Bi & Shaohua Pan

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Jein-Shan Chen

Authors
  1. Shujun Bi
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  2. Shaohua Pan
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  3. Jein-Shan Chen
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Correspondence to Jein-Shan Chen.

Additional information

J.-S. Chen is Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office.

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Bi, S., Pan, S. & Chen, JS. The same growth of FB and NR symmetric cone complementarity functions. Optim Lett 6, 153–162 (2012). https://doi.org/10.1007/s11590-010-0257-z

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  • DOI: https://doi.org/10.1007/s11590-010-0257-z

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