一类非线性二层规划的Frank-Wolfe方法

Frank-Wolfe method for solving a class of nonlinear bilevel programming problem

利用下层问题的K-T最优性条件将下层为线性规划的一类非线性二层规划转化为相应的单层规划,同时取互补条件为罚项,得到该类问题的单层罚问题;然后利用Frank-Wolfe方法对单层罚问题进行求解.数值实验表明该方法是可行的.

By using the K-T optimality condition of the lower level problem,a class of nonlinear bilevel programming problem was transformed into a corresponding single level programming and the complementary condition was append to the upper level objective with a penalty.Then the Frank-Wolfe approach was applied to solve this kind of problem and an example was solved to illustrate this approach.