A Primal-Dual Interior Point Method For Optimization Problems With Nonlinear Complementarity Constraints

This dissertation discusses mathematical program with nonlinear complementarity constraints. Complementarity constrained optimization is an important class of constrained optimization problems, which has some widely applications in the field of economics, engineering design, decision-making and countermeasures, traffic transportation.In this dissertation, we propose a new primal-dual interior point method for special of optimization problems with nonlinear compementa--ity constraints. Main ideas of the algorithm are as follows:firstly, by a generalized complementarity function, the disscussed problem is transformed into a family of nonlinear optimization problems. Then we introduce a special form of penalty function as a merit function and combining with the new active set identification to a primal-dual interior point algorithm for the disscussed problem. At each iteration, the method needs to solve two or three reduced systems of linear equations with the same coefficient matrix and the computational cost of calculations is less than SQP’S. Lastly, we use a weaker condition on approximate Hessian of the Lagrangian in the new algorithm. Under some mild conditions the algorithm is proved to be globally and superlinearly convergencent. At the end of the dissertation, promising numerical results are reported.