一个非光滑凸规划问题的可执行束方法

摘要

本文研究了求解无约束凸规划问题的迫近束方法.首先,我们给出一般束方法.然后,提出迫近参数的一种新的更新策略.在第k次迭代时,如果实际下降量与期望下降量很接近,则扩大迫近参数,反之缩小迫近参数.进而,研究包含次梯度聚集策略和迫近参数更新策略的可执行束方法及其收敛性分析.最后,通过两个数值算例验证了算法的有效性.%An implementable bundle method for unconstrained nonsmooth convex optimization problem is provided in this paper.At first,a general bundle method is given.Next,a new update strategy for the proximal parameter is proposed.At the kth iteration,if the actual descent is close to the predicted one,the proximal parameter is enlarged;otherwise,it is decreased.Then,an implementable bundle method is proposed,which combines the subgradient aggregation strategy with the proximal parameter update strategy.At the same time,its convergence analysis is given as well.Finally,two numerical examples are presented to show the validity of the algorithm proposed in this paper.