The H-differentiability and calmness of circular cone functions

Let $$\mathcal{L}_{\theta }$$Lθ be the circular cone in $${\mathbb {R}}^n$$Rn which includes second-order cone as a special case. For any function f from $${\mathbb {R}}$$R to $${\mathbb {R}}$$R, one can define a corresponding vector-valued function $$f^{\mathcal{L}_{\theta }}$$fLθ on $${\mathbb {R}}^n$$Rn by applying f to the spectral values of the spectral decomposition of $$x \in {\mathbb {R}}^n$$x∈Rn with respect to $$\mathcal{L}_{\theta }$$Lθ. The main results of this paper are regarding the H-differentiability and calmness of circular cone function $$f^{\mathcal{L}_{\theta }}$$fLθ. Specifically, we investigate the relations of H-differentiability and calmness between f and $$f^{\mathcal{L}_{\theta }}$$fLθ. 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.