A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

摘要

In this paper, based on the smoothing techniques and the working set techniques, a QP-free algorithm for mathematical programs with equilibrium constraints (MPEC for short) is presented. Firstly, by Fischer–Burmeister function and smoothing techniques, the discussed problem is approximated by a smooth constrained optimization problem. Secondly, the working set, which is used to construct systems of linear equations, is generated by pivoting operation. At each iteration, the search direction is yielded by solving two or three systems of equations with the same coefficient matrix. Under mild conditions, the global convergence and superlinear convergence are shown. Moreover, we can conclude that the current iterative point is an exact stationary point of the discussed problem if the proposed algorithm stops after finite iterations. Finally, preliminary numerical results are reported.