TY - JOUR
T1 - A Regularization Semismooth Newton Method for $P_0$-NCPs with a Non-Monotone Line Search
AU - Li-Yong Lu, Wei-Zhe Gu & Wei Wang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 186
EP - 204
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2012.m10027
UR - https://global-sci.org/intro/article_detail/nmtma/5934.html
KW - Nonlinear complementarity problem, non-monotone line search, semismooth Newton method, global convergence, local superlinear convergence.
AB - <p style="text-align: justify;">In this paper, we propose a regularized version of the generalized
NCP-function proposed by Hu, Huang and Chen [J. Comput. Appl. Math., 230 (2009),
pp. 69-82]. Based on
this regularized function, we propose a semismooth Newton method for
solving nonlinear complementarity problems, where a non-monotone
line search scheme is used. In particular, we show that the proposed
non-monotone method is globally and locally superlinearly
 convergent under suitable assumptions. We test the
proposed method by solving the test problems from MCPLIB. 
Numerical experiments indicate that this algorithm has better
numerical performance in the case of $p=5$ and $\theta\in[0.25,075]$&nbsp; than other cases.</p>