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 59 articles , 1 standard article )

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  1. Dong, Li; Tang, Jingyong; Song, Xinyu: A non-monotone inexact non-interior continuation method based on a parametric smoothing function for LWCP (2018)
  2. Tang, Jingyong; Zhou, Jinchuan; Fang, Liang: Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP (2018)
  3. Liu, Ruijuan: A new smoothing and regularization Newton method for the symmetric cone complementarity problem (2017)
  4. Miao, Xin-He; Chang, Yu-Lin; Chen, Jein-Shan: On merit functions for $p$-order cone complementarity problem (2017)
  5. Miao, Xin-He; Yang, Jian-Tao; Saheya, B.; Chen, Jein-Shan: A smoothing Newton method for absolute value equation associated with second-order cone (2017)
  6. Miao, Xin-He; Guo, Shengjuan; Qi, Nuo; Chen, Jein-Shan: Constructions of complementarity functions and merit functions for circular cone complementarity problem (2016)
  7. Miao, Xin-He; Lin, Yen-chi Roger; Chen, Jein-Shan: An alternative approach for a distance inequality associated with the second-order cone and the circular cone (2016)
  8. Chen, Shuang; Pang, Li-Ping; Li, Dan: An inexact semismooth Newton method for variational inequality with symmetric cone constraints (2015)
  9. Hao, Zijun; Wan, Zhongping; Chi, Xiaoni; Chen, Jiawei: A power penalty method for second-order cone nonlinear complementarity problems (2015)
  10. Kong, Lingchen; Sun, Jie; Tao, Jiyuan; Xiu, Naihua: Sparse recovery on Euclidean Jordan algebras (2015)
  11. Liu, Lixia; Liu, Sanyang; Wu, Yan: A smoothing Newton method for symmetric cone complementarity problem (2015)
  12. Seeger, Alberto; Sossa, David: Complementarity problems with respect to Loewnerian cones (2015)
  13. 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)
  14. Gu, Wei-Zhe; Huang, Zheng-Hai: A homogeneous smoothing-type algorithm for symmetric cone linear programs (2014)
  15. Lu, Nan; Huang, Zheng-Hai: A smoothing Newton algorithm for a class of non-monotonic symmetric cone linear complementarity problems (2014)
  16. Tang, Jingyong; Dong, Li; Zhou, Jinchuan; Fang, Liang: A new non-interior continuation method for solving the second-order cone complementarity problem (2014)
  17. Wang, Yong; Zhao, Jian-Xun: An algorithm for a class of nonlinear complementarity problems with non-Lipschitzian functions (2014)
  18. Zhang, Lei-Hong; Yang, Wei Hong: An efficient algorithm for second-order cone linear complementarity problems (2014)
  19. Chi, Xiaoni; Wan, Zhongping; Hao, Zijun: A two-parametric class of merit functions for the second-order cone complementarity problem (2013)
  20. Tang, Jingyong; Dong, Li; Fang, Liang; Zhou, Jinchuan: The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem (2013)

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