On the H-differentiability of löwner function with application in symmetric cone complementarity problem

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Abstract

Let K be the symmetric cone in a Jordan algebra ¥. For any function f from ]R to 1R,one can define the corresponding Löwner function fsc(x) on ¥ by the spectral decomposition of x ε ¥ with respect to 1C. In this paper, we study the relationship regarding. H-differentiability between fsc and f. The class of if-differentiable functions is known to be wider than the class of semismooth functions. Therefore, our result will contribute to solution analysis and solution methods for solving more general symmetric cone programs (SCP) and symmetric cone complementarity problems (SCCP). Besides, we also studya merit function approach for SCCP under H-differentiable condition. In particular, forsuch class of complementarity problems, we provide conditions to guarantee every stationary point ofthe associated merit function to be a solution.

Original languageEnglish
Pages (from-to)231-243
Number of pages13
JournalJournal of Nonlinear and Convex Analysis
Volume14
Issue number2
Publication statusPublished - 2013 Apr

Keywords

  • Complementarity
  • If-Differentiable
  • Second-order cone
  • Symmetric cone

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

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