基于近似一阶信息的改进的加速水平束方法

An Modified Accelerated Level Bundle Method Based on Approximate First Order Information

本文提出了一个近似一阶信息的改进的加速水平束方法,该方法结合多步加速策略,引入了三个迭代点序列进行求解,通过引入非欧氏距离代替传统的欧式距离,从而可以充分利用可行集的几何集合,与Lan的方法相比,本文提出的方法仅需求解一个子问题,从而可以减少算法的计算量。最后对所提出的算法进行收敛性分析以及计算相应的迭代复杂度。

In this paper, we propose an improved acceleration level bundle method with approximate first-order information, which combines the multistep acceleration strategy and introduces three iterative point sequences to solve, and can make full use of the geometric set of feasible sets by introducing non-Euclidean distances instead of traditional Euclidean distances. Finally, Global convergence of the algorithm is proved and the iterative complexity is analyzed.