The H-differentiability and calmness of circular cone functions

Jinchuan Zhou (), Yu-Lin Chang () and Jein-Shan Chen ()

Journal of Global Optimization, 2015, vol. 63, issue 4, 833 pages

Abstract: Let $$\mathcal{L}_{\theta }$$ L θ be the circular cone in $${\mathbb {R}}^n$$ R n 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 $$f^{\mathcal{L}_{\theta }}$$ f L θ on $${\mathbb {R}}^n$$ R n by applying f to the spectral values of the spectral decomposition of $$x \in {\mathbb {R}}^n$$ x ∈ R n with respect to $$\mathcal{L}_{\theta }$$ L θ . The main results of this paper are regarding the H-differentiability and calmness of circular cone function $$f^{\mathcal{L}_{\theta }}$$ f L θ . Specifically, we investigate the relations of H-differentiability and calmness between f and $$f^{\mathcal{L}_{\theta }}$$ f L θ . 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. Copyright Springer Science+Business Media New York 2015

Keywords: Circular cone; H-differentiable; Calmness; 26A27; 26B05; 26B35; 49J52; 90C33; 65K05 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10898-015-0312-5

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