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 77 articles , 1 standard article )

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  1. Ke, Yifen: The matrix splitting iteration method for nonlinear complementarity problems associated with second-order cone (2021)
  2. Miao, Xin-He; Chen, Jein-Shan: On matrix characterizations for (P)-property of the linear transformation in second-order cone linear complementarity problems (2021)
  3. Jiang, Xiaoqin; Huang, He: A smoothing Newton method with a mixed line search for monotone weighted complementarity problems (2020)
  4. Liu, Xiangjing; Liu, Sanyang: A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian (P_0)-property (2020)
  5. Tang, Jingyong; Zhou, Jinchuan: Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones (2020)
  6. Chen, Shuang; Pang, Li-ping; Li, Dan; Wang, Jin-he: An inexact modified Newton method for VISCC and application in grasping force (2019)
  7. Liu, Sanyang; Liu, Xiangjing; Chen, Junfeng: A projection and contraction method for symmetric cone complementarity problem (2019)
  8. Nguyen, Chieu Thanh; Saheya, B.; Chang, Yu-Lin; Chen, Jein-Shan: Unified smoothing functions for absolute value equation associated with second-order cone (2019)
  9. Tang, Jingyong; Huang, Chengdai; Wang, Yongli: Predictor-corrector inexact smoothing algorithm for symmetric cone complementarity problems with Cartesian (P_0)-property (2019)
  10. Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang: An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem (2019)
  11. Dong, Li; Tang, Jingyong; Song, Xinyu: A non-monotone inexact non-interior continuation method based on a parametric smoothing function for LWCP (2018)
  12. Dong, Li; Tang, Jingyong; Song, Xinyu: Numerical study of a smoothing algorithm for the complementarity system over the second-order cone (2018)
  13. Ke, Yi-Fen; Ma, Chang-Feng; Zhang, Huai: The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems (2018)
  14. Ke, Yi-Fen; Ma, Chang-Feng; Zhang, Huai: The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems (2018)
  15. Tang, Jingyong; Zhou, Jinchuan; Fang, Liang: Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP (2018)
  16. Zhao, Huali; Liu, Hongwei: Iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones (2018)
  17. Liu, Ruijuan: A new smoothing and regularization Newton method for the symmetric cone complementarity problem (2017)
  18. Miao, Xin-He; Chang, Yu-Lin; Chen, Jein-Shan: On merit functions for (p)-order cone complementarity problem (2017)
  19. 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)
  20. Miao, Xin-He; Guo, Shengjuan; Qi, Nuo; Chen, Jein-Shan: Constructions of complementarity functions and merit functions for circular cone complementarity problem (2016)

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