Numerical Functional Analysis and Optimization, vol. 32, pp. 507-523, 2011 On the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space Xin-He Miao 1 Department of Mathematics School of Science Tianjin University Tianjin 300072, P.R. China Jein-Shan Chen 2 Department of Mathematics National Taiwan Normal University Taipei 11677, Taiwan October 26, 2010 (revised on February 14, 2011) Abstract In this paper, we consider the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. We establish several results which 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. Key words. Lorentz cone, FB-function, NR-function, merit function, error bound, R 02 - property. 1 also affiliated with Department of Mathematics, National Taiwan Normal University as a postdoc fellow. E-mail: xinhemiao@tju.edu.cn 2 Corresponding author. Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan. E-mail: jschen@math.ntnu.edu.tw. 1