| As we know, optimization problems with complementarity constraints have a wide application in economy, engineering design, game theory, making decision and so on, so in recent years there has been a growing literature on these important optimization problems.In this paper, we discuss a special kind of optimization problems with complementarity constraints, in which the constraints are defined by a linear complementarity(LCP for short). In early stage, some scholars attempted to solve it by means of transforming it into a standard smooth nonlinear problem (SSNP for short). But J.V.Outrata, M.Kocvara, et.al. pointed out in 1998 that the equivalent SSNP didn't satisfy the weaker Mangasarian-Fromotitz constraint qualification in any feasible points. So it will be very difficult to get the solution of LCP by means of existing methods for SSNP such as sequential quadratic programming (SQP for short) type algorithms, sequential systems of linear equations (SSLE for short) type algorithms.In this paper, we present a new algorithm for LCP-SSLE algorithm. The main idea of the algorithm is as follows: at first, by means of a generalized complementarity function and per-turbative technique, we transform the discussed problem into a cluster of general nonlinear optimization problems containing aparameter. Secondly, by using a special penalty function as merit function, we establish a sequential system of linear equations algorithm. Because three systems of equations solved at each iteration have the same coefficients, so the ammount of computation are less than that of the existing SQP algorithms. Under some common conditions (such as the second order sufficient condition) which are used in some references , we prove that the algorithm possesses not only global convergence, but also strong convergence and superlinear convergence. At the end of the paper, some preliminary numerical experiments are given. The numerical results shoew that the algorithm is effective.
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