### 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 f^{sc}(x) on ¥ by the spectral decomposition of x ε ¥ with respect to 1C. In this paper, we study the relationship regarding. H-differentiability between f^{sc} 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 language | English |
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Pages (from-to) | 231-243 |

Number of pages | 13 |

Journal | Journal of Nonlinear and Convex Analysis |

Volume | 14 |

Issue number | 2 |

Publication status | Published - 2013 Apr |

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### Keywords

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

### ASJC Scopus subject areas

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