论文标题
关于具有相对误差规则的不精确加速近端方法
On Inexact Accelerated Proximal Gradient Methods with Relative Error Rules
论文作者
论文摘要
最受欢迎，最重要的一阶迭代之一，可提供经典近端梯度方法（PGM）的最佳复杂性，是“快速迭代收缩/阈值算法”（FISTA）。在本文中，研究了两个用于最小化两个凸函数总和的不精确版本。所提出的方案不截然不见地通过使用相对误差标准而不是外源性和减少误差规则来解决其子问题。当困难近端运算符的评估时，Fista的不精确版本是必需的，并且此处提出的相对错误规则可能比以前的错误规则具有某些优势。对于两种提出的方案，均回收了相同的FISTA的最佳收敛速率。据报道，一些数值实验说明了新方法的数值行为。
One of the most popular and important first-order iterations that provides optimal complexity of the classical proximal gradient method (PGM) is the "Fast Iterative Shrinkage/Thresholding Algorithm" (FISTA). In this paper, two inexact versions of FISTA for minimizing the sum of two convex functions are studied. The proposed schemes inexactly solve their subproblems by using relative error criteria instead of exogenous and diminishing error rules. When the evaluation of the proximal operator is difficult, inexact versions of FISTA are necessary and the relative error rules proposed here may have certain advantages over previous error rules. The same optimal convergence rate of FISTA is recovered for both proposed schemes. Some numerical experiments are reported to illustrate the numerical behavior of the new approaches.
