乘子方法中的参数选择

Di Pillo和Grippo提出的含参数C〉0的增广Lagrangian函数中，使用了最大函数，该函数可能在无穷多个点处不可微．为了克服这个问题，濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性；同时该方法具有全局收敛性，且在适当假设下，具有超线性收敛率．但是在该方法中，要求参数C充分大．为了实现算法及提高算法效率，本文给出了一个有效选择参数C的方法．

Choosing Parameter in Multiplier Method

Di Pillo and Grippo proposed a class of augmented Lagrangian function methods with a max function which may be not differentiable at infinite points. To overcome this shortcoming, a new class of augmented Lagrangian functions with the Fischer-Burmeister NCP function and some Lagrangian multiplier method is proposed for the minimization of a smooth function subject to smooth equation and inequality constraints. This method is an iterative method in which, locally, the iteration can be viewed as the Newton or quasi Newton iteration; and this method is globally convergent. However, a parameter C is required to be large enough in this method, and this requirement makes the method implementable. In order to realize this method, we we construct a function to adjust the parameter in the augmented Lagrangian function, and get the smallest feasible C in the programm.