Let Lθ be the circular cone in Rn which includes a second-order cone as a special case. For any function f from R to R, one can define a corresponding vector-valued function fc(x) on Rn by applying f to the spectral values of the spectral decomposition of x ⋯ Rn with respect to Lθ. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as semismoothness. These results will play a crucial role in designing solution methods for optimization problem associated with the circular cone.
|Number of pages||14|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2013 Apr 3|
- Circular cone Vector-valued function Semismooth function Complementarity Spectral decomposition
ASJC Scopus subject areas
- Applied Mathematics