TY - JOUR
T1 - On the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space
AU - Miao, Xin He
AU - Chen, Jein Shan
N1 - Funding Information:
Received 26 October 2010; Revised and Accepted 14 February 2011. J.-S. C. is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. This author’s work is partially supported by National Science Council of Taiwan. Address correspondence to Jein-Shan Chen, Department of Mathematics, National Taiwan Normal University, 88, Section 4, Ting Chou Road, Taipei 11677, Taiwan; E-mail: [email protected]
PY - 2011/5
Y1 - 2011/5
N2 - In this article, we consider the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. We establish several results that are standard and important when dealing with complementarity problems. These include proving the same growth of the Fishcher-Burmeister merit function and the natural residual merit function, investigating property of bounded level sets under mild conditions via different merit functions, and providing global error bounds through the proposed merit functions. Such results are helpful for further designing solution methods for the Lorentz cone complementarity problems in Hilbert space.
AB - In this article, we consider the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. We establish several results that are standard and important when dealing with complementarity problems. These include proving the same growth of the Fishcher-Burmeister merit function and the natural residual merit function, investigating property of bounded level sets under mild conditions via different merit functions, and providing global error bounds through the proposed merit functions. Such results are helpful for further designing solution methods for the Lorentz cone complementarity problems in Hilbert space.
KW - Error bound
KW - FB-function
KW - Lorentz cone
KW - Merit function
KW - NR-function
KW - R -property
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U2 - 10.1080/01630563.2011.563893
DO - 10.1080/01630563.2011.563893
M3 - Article
AN - SCOPUS:79953701954
SN - 0163-0563
VL - 32
SP - 507
EP - 523
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 5
ER -