Filter Trust Region Algorithms And Multiplier Algorithms For Nonlinear Bilevel Programs

In this article, we disscuss the solving algorithms for the nonlinear bilevel pro-grams. This paper mainly consists of two parts.In the first part, motivated by the trust region subproblem, we present a filter trust region algorithms for the nonlinear bilevel programs. We construct first a special quadratic model for nonlinear bilevel programmings. Then we try to slove the model in the filter trust region based on the norm l1, and the solution of the model then is acted as the start point of the next iterative. Meanwhile, an example is given to illustrate effectivity of the algorithm (FT).In the second part, we propose another solving algorithm for the problem pre-sented in the first part. Thanks to the detailed descriptions in the first part, we observe that the bilevel programming can be transformed into a single level pro-gramming. Due to the particular structure of the problem, we design a multiplier algorithm (CZ) to solve it, which is based on the nonmonotonic technique. We fur-ther give an example to illustrate effectivity of the algorithm. Finally, we give the related proof about its convergence.