TY - JOUR
T1 - The same growth of FB and NR symmetric cone complementarity functions
AU - Bi, Shujun
AU - Pan, Shaohua
AU - Chen, Jein Shan
N1 - Funding Information:
Acknowledgments S. Pan’s work was supported by National Young Natural Science Foundation (No. 10901058) and Guangdong Natural Science Foundation (No. 9251802902000001) and the Fundamental Research Funds for the Central Universities (SCUT). J.-S. Chen’s work was supported by National Science Council of Taiwan.
PY - 2012/1
Y1 - 2012/1
N2 - 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.
AB - 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.
KW - FB and NR complementarity functions
KW - Growth
KW - Symmetric cone
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U2 - 10.1007/s11590-010-0257-z
DO - 10.1007/s11590-010-0257-z
M3 - Article
AN - SCOPUS:84855222569
SN - 1862-4472
VL - 6
SP - 153
EP - 162
JO - Optimization Letters
JF - Optimization Letters
IS - 1
ER -