Abstract: The nonlinear complementarity problem can be reformulated as a nonlinear programming. This paper proposes a feasible SQP method with nonmonotone line search, and obtains a feasible descent direction by  full use of the K-T point pair of a QP subproblem without other additional cost. A high-order direction is computed to overcome the Maratos effect. Instead of filter method,   a nonmonotone line search is used to obtain the step length. Under some suitable conditions, not including the strict complementary condition,  the global convergence of the algorithm is obtained. Some numerical results are also reported in this paper.

Key words: constrained , optimization, sequential quardratic, programming, active set, nonmonotone technique, global convergence