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