A New Qp-free Algorithm For Optimization With Nonlinear Complementarity Constraints

Mathematical program with equilibrium constraints (MPEC for short), is a special kind of constrained optimization problem. MPEC has a strong practical background and widely applications in engineering design, transportation, communication, economic and other fields. Therefore, the research on MPEC has an important significance.In this dissertation, by means of "working set" technique for determining the active set and the idea of sequential system of linear equations, a new QP-free algorithm for solving nonlinear complementarity constrained optimization problem is presented. The main ideas of the algorithm are as follows:firstly, by the introduction of a generalized complementary function, the discussed problem can be transformed equivalently into the general constrained optimization problem; Secondly, sequential systems of linear equations are constructed by combining working set technique and the search directions are determined by the solving two or three sequential systems of linear equations with the same coefficient matrix. Finally, the global convergence, strong convergence and superlinear convergence are analyzed under some appropriate assumptions.The proposed algorithm in this dissertation has the following advantages: the initial point is chosen arbitrarily. Due to the introduction of working set, the scale of the sequential system of linear equations becomes smaller and the computation cost is decreased. The proposed algorithm possesses not only global convergence, but also strong convergence and superlinear convergence under some appropriate conditions.