A superlinearly convergent SQP algorithm for mathematical programs with linear complementarity constraints

In this paper, MPEC problems with linear complementarity constraints are considered. By means of Fischer-Burmeister function, the linear complementarity condition is transformed into a nonsmooth equation. Then, during the iteration, a corresponding smooth system approximates the nonsmooth equation. The smooth optimization is solved by SQP algorithm for standard constrained optimization. Global convergence and superlinear convergence rate are established under some suitable assumptions. Moreover, we conclude that the current iterate point is an exact stationary point of the MPEC problem when the proposed algorithm stops in finite iteration.