Appl Math Optim 53:79–100 (2006)
2005 Springer Science+Business Media, Inc.
A New Noninterior Predictor–Corrector Method for the P
and Jian Chen
Chinese Academy of Sciences Research Center on
Data Technology & Knowledge Economy;
Graduate University of the Chinese Academy of Sciences,
Chinese Academy of Sciences, Beijing 100080, China
Department of Management Science and Engineering,
School of Economics and Management, Tsinghua University,
Beijing 100084, China
Abstract. In this paper a new predictor–corrector noninterior method for LCP
is presented, in which the predictor step is generated by the Levenberg–Marquadt
method, which is new in the predictor–corrector-type methods, and the corrector
step is generated as in . The method has the following merits: (i) any cluster point
of the iteration sequence is a solution of the P
LCP; (ii) if the generalized Jacobian
is nonsingular at a solution point, then the whole sequence converges to the (unique)
solution of the P
LCP superlinearly; (iii) for the P
LCP, if an accumulation point of
the iteration sequence satisﬁes the strict complementary condition, then the whole
sequence converges to this accumulation point superlinearly. Preliminary numerical
experiments are reported to show the efﬁciency of the algorithm.
Key Words. LCP, Predictor–corrector method, Smoothing technique, Superlinear
AMS Classiﬁcation. 90C33, 65K10.
Consider the following linear complementary problem (LCP):
y = Mx+ q,
x ≥ 0, y ≥ 0, x
y = 0, (1)
This work was supported in part by the National Natural Science Foundation of China (Grant No.
70071015, 70321001, 70302003).