The H-differentiability and calmness of circular cone functions

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• 作者：Jinchuan Zhou ; Yu-Lin Chang ; Jein-Shan Chen
• 关键词：Circular cone ; H ; differentiable ; Calmness ; 26A27 ; 26B05 ; 26B35 ; 49J52 ; 90C33 ; 65K05
• 刊名：Journal of Global Optimization
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：63
• 期：4
• 页码：811-833
• 全文大小：541 KB
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• 作者单位：Jinchuan Zhou (1)
  Yu-Lin Chang (2)
  Jein-Shan Chen (2)
  
  1. Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, People鈥檚 Republic of China
  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Science, general
  Real Functions
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1573-2916

文摘

Let \(\mathcal{L}_{\theta }\) be the circular cone in \({\mathbb {R}}^n\) which includes second-order cone as a special case. For any function f from \({\mathbb {R}}\) to \({\mathbb {R}}\), one can define a corresponding vector-valued function \(f^{\mathcal{L}_{\theta }}\) on \({\mathbb {R}}^n\) by applying f to the spectral values of the spectral decomposition of \(x \in {\mathbb {R}}^n\) with respect to \(\mathcal{L}_{\theta }\). The main results of this paper are regarding the H-differentiability and calmness of circular cone function \(f^{\mathcal{L}_{\theta }}\). Specifically, we investigate the relations of H-differentiability and calmness between f and \(f^{\mathcal{L}_{\theta }}\). 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. Keywords Circular cone H-differentiable Calmness