一类多维滤子信赖域方法的收敛性

Global Convergence of a Multi-dimension Filter Trust Region Method

滤子方法是一类无需罚函数的方法,它具有良好的数值结果,因此近年来该方法已应用于各种优化问题的求解中。基于滤子方法的有效性和信赖域技巧的强适性,提出了一个多维的滤子信赖域方法,该方法在一定程度上避免了Marotos效应。本文针对这类多维滤子信赖域方法的收敛性进行讨论,得到了该算法是可行并且是全局收敛的,使得新的算法能够得以有效的应用。

Filter method is a kind of no penalty-function method.Because of promosing numerical results,it is recently applied to all kinds of optimization problems.Based on the efficiency of filter techniques and the robustness of trust-region method,a new multi-dimension trust region filter method is proposed.In some cases,the Marotos effect can be avoid.The convergences of the proposed method are studied and global convergence properties are obtained.So the new algorithm is effective and convergent.