Appl Math Optim 47:195–211 (2003)
2003 Springer-Verlag New York Inc.
Non-Interior Continuation Method for Solving the Monotone
Semideﬁnite Complementarity Problem
Zhenghai Huang and Jiye Han
Institute of Applied Mathematics,
Academy of Mathematics and System Sciences,
Chinese Academy of Sciences,
Beijing, 100080, P.O. Box 2734, People’s Republic of China
Abstract. Recently, Chen and Tseng extended non-interior continuation/smooth-
ing methods for solving linear/nonlinear complementarity problems to semideﬁnite
complementarity problems (SDCP). In this paper we propose a non-interior con-
tinuation method for solving the monotone SDCP based on the smoothed Fischer–
Burmeister function, which is shown to be globally linearly and locally quadratically
convergent under suitable assumptions. Our algorithm needs at most to solve a linear
system of equations at each iteration. In addition, in our analysis on global linear
convergence of the algorithm, we need not use the assumption that the Fr´echet deriva-
tive of the function involved in the SDCP is Lipschitz continuous. For non-interior
continuation/smoothing methods for solving the nonlinear complementarity prob-
lem, such an assumption has been used widely in the literature in order to achieve
global linear convergence results of the algorithms.
Key Words. Monotone semideﬁnite complementarity problem, Non-interior con-
tinuation method, Global linear convergence, Local quadratic convergence.
AMS Classiﬁcation. 65K05, 90C25, 90C33.
Let ℵ denote the space of n × n block-diagonal real matrices with m blocks of sizes
, respectively (the blocks are ﬁxed), let S denote the subspace comprising
This project was supported by the National Nature Science Foundation of China (Grants 19731001 and