Malitsky Yu
Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria.
Optim Methods Softw. 2017 Mar 21;33(1):140-164. doi: 10.1080/10556788.2017.1300899. eCollection 2018.
The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also, the methods do not require Lipschitz continuity of the operator and the linesearch procedure uses only values of the operator. Moreover, when the operator is affine our linesearch becomes very simple, namely, it needs only simple vector-vector operations. For all our methods, we establish the ergodic convergence rate. In addition, we modify one of the proposed methods for the case of a composite minimization. Preliminary results from numerical experiments are quite promising.
本文关注单调变分不等式的新型一阶方法。它们使用一种非常简单的线搜索过程，该过程考虑了算子的局部信息。此外，这些方法不需要算子的Lipschitz连续性，并且线搜索过程仅使用算子的值。而且，当算子是仿射的时候，我们的线搜索变得非常简单，即只需要简单的向量 - 向量运算。对于我们所有的方法，我们建立了遍历收敛速率。此外，我们针对复合最小化的情况修改了其中一种提出的方法。数值实验的初步结果很有前景。
