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TopIntroduction
The nonlinear complementarity problem (NCP) is to determine a vector
such that
(1) where

is a nonlinear mapping. Throughout this paper we assume that

is continuous and monotone with respect to

and the solution set of (1) is nonempty. NCP has many important applications in engineering, economics, military operations planning, finance, medical treatment, supply chain management etc, (Auslender & Haddou, 1995; Das, 2009; Castagnoli & Favero, 2008; Ferris & Pang, 1997; Harker & Pang, 1990; Yan & Wang, 1997). Many numerical methods for solving NCP have been developed (Auslender & Haddou, 1995; Auslender et al., 1999; Bnouhachem & Noor, 2001; Burachik & Svaiter, 2001; Censor et al., 1994; Eckstein, 1998; Fischer, 1997; Guler, 1991; Iusem, 1998; Pang, 1995; Qi & Yang, 2002; Sun & Qi, 1999; Zhou, 2009).
NCP can be alternatively formulated as finding the zero point of an appropriate maximal monotone operator
(2) i.e., finding

such that

, where

is the normal cone operator to

defined by
(3)A well known method to find the zero point of a maximal monotone operator
is the proximal point algorithm (PPA), which starts with any vector
and
and iteratively updates
conforming the following problem:
(4)In order to obtain the new point
, the subproblem (1.4) of PPA is equivalent to the following variational inequality problem:
Find
such that
(5)