以下层问题的最优性条件代替下层问题, 将下层为凸标量优化的一类二层多目标规划问题转化为带互补约束的不可微多目标规划问题, 采用扰动的Fischer-Burmeister函数对互补约束光滑化, 得到了相应的光滑化多目标规划问题, 分析了原问题的有效解与光滑化多目标规划问题有效解的关系, 设计了求解该类二层多目标规划问题的光滑化算法, 并分析了算法的收敛性. 数值结果表明该光滑化方法是可行的.

Using the method of replacing the lower level programs with its optimality conditions, we transform a class of bilevel multiobjective programs, where the lower level is a convex scalar program and the upper level is a vector program, into an equivalent one-level nonsmooth multiobjective programs. Then, we use the perturbed Fischer-Burmeister function to smooth the complementary conditions to obtain a problem of smooth multiobjective programs. Furthermore, we analyze the relationships between the efficient solutions of the original programs and the smoothing programs,propose a smoothing algorithm and analyze the convergence of the algorithm. Finally, a numerical result shows that the algorithm is feasible and efficient.