SCCP

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 66 articles , 1 standard article )

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  1. Nguyen, Chieu Thanh; Saheya, B.; Chang, Yu-Lin; Chen, Jein-Shan: Unified smoothing functions for absolute value equation associated with second-order cone (2019)
  2. Dong, Li; Tang, Jingyong; Song, Xinyu: Numerical study of a smoothing algorithm for the complementarity system over the second-order cone (2018)
  3. Dong, Li; Tang, Jingyong; Song, Xinyu: A non-monotone inexact non-interior continuation method based on a parametric smoothing function for LWCP (2018)
  4. Ke, Yi-Fen; Ma, Chang-Feng; Zhang, Huai: The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems (2018)
  5. Ke, Yi-Fen; Ma, Chang-Feng; Zhang, Huai: The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems (2018)
  6. Tang, Jingyong; Zhou, Jinchuan; Fang, Liang: Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP (2018)
  7. Zhao, Huali; Liu, Hongwei: Iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones (2018)
  8. Liu, Ruijuan: A new smoothing and regularization Newton method for the symmetric cone complementarity problem (2017)
  9. Miao, Xin-He; Chang, Yu-Lin; Chen, Jein-Shan: On merit functions for $p$-order cone complementarity problem (2017)
  10. 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)
  11. Miao, Xin-He; Guo, Shengjuan; Qi, Nuo; Chen, Jein-Shan: Constructions of complementarity functions and merit functions for circular cone complementarity problem (2016)
  12. 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)
  13. Chen, Shuang; Pang, Li-Ping; Li, Dan: An inexact semismooth Newton method for variational inequality with symmetric cone constraints (2015)
  14. Hao, Zijun; Wan, Zhongping; Chi, Xiaoni: A power penalty method for second-order cone linear complementarity problems (2015)
  15. Hao, Zijun; Wan, Zhongping; Chi, Xiaoni; Chen, Jiawei: A power penalty method for second-order cone nonlinear complementarity problems (2015)
  16. Kong, Lingchen; Sun, Jie; Tao, Jiyuan; Xiu, Naihua: Sparse recovery on Euclidean Jordan algebras (2015)
  17. Liu, Lixia; Liu, Sanyang; Wu, Yan: A smoothing Newton method for symmetric cone complementarity problem (2015)
  18. Li, Yuan-Min; Wei, Deyun: A generalized smoothing Newton method for the symmetric cone complementarity problem (2015)
  19. Seeger, Alberto; Sossa, David: Complementarity problems with respect to Loewnerian cones (2015)
  20. 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)

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