Theory And Algorithm Study Of Two Kinds Of Nonlinear Bilevel Programming

In this article, we disscuss the optimal solutions and solving algorithms for the nonlinear bilevel programming. This paper mainly consists of two parts. In the first part, motivated by the DC programming, we consister a class of nonlinear bilevel programs in which the objective function in the first level is a DC function and the second level consists of a set of KKT points of a quadratic programming. By combining DCA and Zoutendijk Feasible Direction Method, an algorithm is given for it, and the computational results of the examples show the feasibility and efficiency of the algorithm.In the second part, we give two algorithms for nonlinear bilevel programming with convex lower level problems. As we know, when the second level is convex, it can be changed into single-level mathematical program by means of KKT con-ditions. With the help of penalty technique, we propose an auxiliary single-level mathematical program which satisfies the linear independence constraint qualifica-tion, and we present a new algorithm and prove its global convergence under some assumptions. We give a numerical example to illustrate feasibility of the algorithm. Using General Reduced Gradient (GRG), we give another simple algorithm for the nonlinear bilevel programming with convex lower level problems.