论文标题
一种用于求解单调包含物并应用于gans的惯性前进算法
A Relaxed Inertial Forward-Backward-Forward Algorithm for Solving Monotone Inclusions with Application to GANs
论文作者
论文摘要
我们引入了一种放松的惯性前向前后（RIFBF）分裂算法，以接近最大单调操作员和单值单调和Lipschitz连续操作员的总和。这项工作旨在通过使用惯性效应和放松参数来扩展Tseng的前回答方法。我们首先制定一个二阶动力系统，该系统接近要解决的单调包含问题的解决方案集并为其轨迹提供渐近分析。我们提供了RIFBF，该RIFBF遵循明确的时间离散化，一般单调元件中的收敛分析，以及应用于伪单声酮变化不平等的解决方案。我们通过应用程序来说明所提出的方法，以在双线性鞍点问题上进行，在这种情况下，我们还强调了惯性和放松参数之间的相互作用，以及对生成对抗网络（GAN）的培训。
We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims to extend Tseng's forward-backward-forward method by both using inertial effects as well as relaxation parameters. We formulate first a second order dynamical system which approaches the solution set of the monotone inclusion problem to be solved and provide an asymptotic analysis for its trajectories. We provide for RIFBF, which follows by explicit time discretization, a convergence analysis in the general monotone case as well as when applied to the solving of pseudo-monotone variational inequalities. We illustrate the proposed method by applications to a bilinear saddle point problem, in the context of which we also emphasize the interplay between the inertial and the relaxation parameters, and to the training of Generative Adversarial Networks (GANs).
