Abstract

Let $$\mathcal{L}_{\theta }$$L? 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 $$f^{\mathcal{L}_{\theta }}$$fL? 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 $$\mathcal{L}_{\theta }$$L?. The main results of this paper are regarding the H-differentiability and calmness of circular cone function $$f^{\mathcal{L}_{\theta }}$$fL?. Specifically, we investigate the relations of H-differentiability and calmness between f and $$f^{\mathcal{L}_{\theta }}$$fL?. 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.

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