Open Access
2014 The Vector-Valued Functions Associated with Circular Cones
Jinchuan Zhou, Jein-Shan Chen
Abstr. Appl. Anal. 2014(SI71): 1-21 (2014). DOI: 10.1155/2014/603542


The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation, which includes second-order cone as a special case when the rotation angle is 45 degrees. Let L θ denote the circular cone in R n . For a function f from R to R , one can define a corresponding vector-valued function f L θ on R n by applying f to the spectral values of the spectral decomposition of x R n with respect to L θ . In this paper, we study properties that this vector-valued function inherits from f , including Hölder continuity, B -subdifferentiability, ρ -order semismoothness, and positive homogeneity. These results will play crucial role in designing solution methods for optimization problem involved in circular cone constraints.


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Jinchuan Zhou. Jein-Shan Chen. "The Vector-Valued Functions Associated with Circular Cones." Abstr. Appl. Anal. 2014 (SI71) 1 - 21, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07022706
MathSciNet: MR3228078
Digital Object Identifier: 10.1155/2014/603542

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI71 • 2014
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