The H-differentiability and calmness of circular cone functions

Let (Formula presented.) be the circular cone in (Formula presented.) which includes second-order cone as a special case. For any function f from (Formula presented.), one can define a corresponding vector-valued function (Formula presented.) on v by applying f to the spectral values of the spectral decomposition of (Formula presented.) with respect to (Formula presented.). The main results of this paper are regarding the H-differentiability and calmness of circular cone function (Formula presented.). Specifically, we investigate the relations of H-differentiability and calmness between f and (Formula presented.). In addition, we propose a merit function approach for solving the circular cone complementarity problems under H-differentiability. These results are crucial to subsequent study regarding various analysis towards optimizations associated with circular cone.