论文标题
单调包含的惯性准Newton方法：有效的分解积分和原始偶型方法
Inertial Quasi-Newton Methods for Monotone Inclusion: Efficient Resolvent Calculus and Primal-Dual Methods
论文作者
论文摘要
我们介绍了一种惯性的准牛顿前回向拆分算法，以解决一类单调包容问题。尽管惯性步骤在计算上是便宜的，但通常，瓶颈是对分解运算符的评估。对度量的更改也使其计算很难（否则在标准度量中）简单运算符。为了充分利用适应度量的优势，我们为低级别的扰动标准度量制定了一种新的有效分辨积分，该计算完全计入了准Newton指标。此外，我们证明了我们的算法的收敛性，包括在两个考虑的操作员之一的情况下，线性收敛速率是强烈单调的。除了一般的单调包含设置之外，我们还实例化了一种新型的惯性准牛顿原始二重混合梯度方法来解决鞍点问题。在图像处理中的几个数值实验中，证明了我们惯性准Newton PDHG方法的有利性能。
We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent operator. A change of the metric makes its computation hard even for (otherwise in the standard metric) simple operators. In order to fully exploit the advantage of adapting the metric, we develop a new efficient resolvent calculus for a low-rank perturbed standard metric, which accounts exactly for quasi-Newton metrics. Moreover, we prove the convergence of our algorithms, including linear convergence rates in case one of the two considered operators is strongly monotone. Beyond the general monotone inclusion setup, we instantiate a novel inertial quasi-Newton Primal-Dual Hybrid Gradient Method for solving saddle point problems. The favourable performance of our inertial quasi-Newton PDHG method is demonstrated on several numerical experiments in image processing.
