The H-differentiability and calmness of circular cone functions

Let Lθ be the circular cone in IR which includes second-order cone as a special case. For any function f from IR to IR, one can define a corresponding vector-valued function fLθ on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Lθ. The main results of this paper are regarding the Hdifferentiability and calmness of circular cone function fLθ . Specifically, we investigate the relations of H-differentiability and calmness between f and fLθ . In addition, we propose a merit function approach for solving the circular cone complementarity problems The author’s work is supported by National Natural Science Foundation of China (11101248, 11271233, 11171247) and Shandong Province Natural Science Foundation (ZR2012AM016). Corresponding author. The author’s work is supported by Ministry of Science and Technology, Taiwan.