| The main content of this thesis is the Approaches for nonlinear bilevel programming which belongs to the bilevel programming. By analyzing the nonlinear bilevel programming model and the nature of the feasible set, starting with the linear-quadratic type we propose two methods for two special classes of nonlinear bilevel programming.Firstly through an example concerned with a toll-setting problem we give the actual background, definitions, feature of the bilevel programming. The special nature of this optimization problem is the hierarchical relationship between two autonomous, and possibly conflict, decision makers. Because of its inherent difficulties, it is hard to solve a bilevel programming. On the one hand, it was proved that the bilevel programming is a NP-hard problem, on the other hand, for some special types, efficient algorithms have been proposed.At present, the methods for nonlinear hebilevel programming generally fall into three categories, branch and bound methods (enumeration), descent methods and penalty function methods. In this paper, we choose the linear-quadratic type as a breakthrough and introduce its conditions of optimization. We transfer it into a mix-integer bilevel programming and solve it.The quadratic bilevel programming is a breakthrough in the study of nonlinear bilevel programming. In real life, the lower decision-makers often have to consider making the square of a function to be optimal, which gives the form of quadratic bilevel programming. The first algorithm is based on the improved rotational steps.Based on the above algorithms, a two-stage method is proposed for a class of nonlinear bilevel programming. At the first phase the descent method is used to reach a small neighborhood of the optimal solution. At the second phase the trust-region method is used. The two-stage method can give full play to the effectiveness of the two algorithms.Finally, the paper summarizes the obtained results and prospects what can be done in the future.
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