Convergence of a non-interior continuation algorithm for the monotone SCCP It is well known that the symmetric cone complementarity problem (SCCP) is a broad class of optimization problems which contains many optimization problems as special cases. Based on a general smoothing function, we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP. The proposed algorithm solves at most one system of linear equations at each iteration. By using the theory of Euclidean Jordan algebras, we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.

References in zbMATH (referenced in 48 articles , 1 standard article )

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  1. Miao, Xin-He; Guo, Shengjuan; Qi, Nuo; Chen, Jein-Shan: Constructions of complementarity functions and merit functions for circular cone complementarity problem (2016)
  2. Hao, Zijun; Wan, Zhongping; Chi, Xiaoni; Chen, Jiawei: A power penalty method for second-order cone nonlinear complementarity problems (2015)
  3. Kong, Lingchen; Sun, Jie; Tao, Jiyuan; Xiu, Naihua: Sparse recovery on Euclidean Jordan algebras (2015)
  4. Liu, Lixia; Liu, Sanyang; Wu, Yan: A smoothing Newton method for symmetric cone complementarity problem (2015)
  5. Seeger, Alberto; Sossa, David: Complementarity problems with respect to Loewnerian cones (2015)
  6. Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang: A Krylov subspace method for large-scale second-order cone linear complementarity problem (2015)
  7. Gu, Wei-Zhe; Huang, Zheng-Hai: A homogeneous smoothing-type algorithm for symmetric cone linear programs (2014)
  8. Lu, Nan; Huang, Zheng-Hai: A smoothing Newton algorithm for a class of non-monotonic symmetric cone linear complementarity problems (2014)
  9. Tang, Jingyong; Dong, Li; Zhou, Jinchuan; Fang, Liang: A new non-interior continuation method for solving the second-order cone complementarity problem (2014)
  10. Wang, Yong; Zhao, Jian-Xun: An algorithm for a class of nonlinear complementarity problems with non-Lipschitzian functions (2014)
  11. Chi, Xiaoni; Wan, Zhongping; Hao, Zijun: A two-parametric class of merit functions for the second-order cone complementarity problem (2013)
  12. Tang, Jingyong; Dong, Li; Fang, Liang; Zhou, Jinchuan: The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem (2013)
  13. Yang, Wei Hong; Yuan, Xiaoming: The GUS-property of second-order cone linear complementarity problems (2013)
  14. Bi, Shujun; Pan, Shaohua; Chen, Jein-Shan: The same growth of FB and NR symmetric cone complementarity functions (2012)
  15. Dong, Li; Tang, Jingyong; Zhou, Jinchuan: A smoothing Newton algorithm for solving the monotone second-order cone complementarity problems (2012)
  16. Kong, Lingchen: Quadratic convergence of a smoothing Newton method for symmetric cone programming without strict complementarity (2012)
  17. Kong, Lingchen; Meng, Qingmin: A semismooth Newton method for nonlinear symmetric cone programming (2012)
  18. Kong, Lingchen; Tunçel, Levent; Xiu, Naihua: Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems (2012)
  19. Li, Yuanmin; Wang, Xingtao; Wei, Deyun: Complementarity properties of the Lyapunov transformation over symmetric cones (2012)
  20. Li, Yuan Min; Wang, Xing Tao; Wei, De Yun: Improved smoothing Newton methods for symmetric cone complementarity problems (2012)

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