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.
|頁（從 - 到）||160-173|
|期刊||Nonlinear Analysis, Theory, Methods and Applications|
|出版狀態||已發佈 - 2013|
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