Smooth and nonsmooth analyses of vector-valued functions associated with circular cones

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• 作者：Yu-Lin Chang ^{ylchang@math.ntnu.edu.tw} ; Ching-Yu Yang ^{yangcy@math.ntnu.edu.tw} ; Jein-Shan Chen ; ^{jschen@ntnu.edu.tw} ; ^{jschen@math.ntnu.edu.tw}
• 关键词：26A27 ; 26B05 ; 26B35 ; 49J52 ; 90C33 ; 65K05
• 刊名：Nonlinear Analysis
• 出版年：2013
• 出版时间：July, 2013
• 年：2013
• 卷：85
• 期：Complete
• 页码：160-173
• 全文大小：555 K

文摘

Let be the circular cone in which includes a second-order cone as a special case. For any function from to , one can define a corresponding vector-valued function on by applying to the spectral values of the spectral decomposition of with respect to . We show that this vector-valued function inherits from the properties of continuity, Lipschitz continuity, directional differentiability, Fr¨¦chet 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.