论文标题
双重梯度方法的收敛速率，用于约束线性不良问题
Convergence rates of a dual gradient method for constrained linear ill-posed problems
论文作者
论文摘要
在本文中，我们考虑了一种求解线性不良问题的双梯度方法$ ax = y $，其中$ a：x \ to y $是来自Banach Space $ x $到Hilbert Space $ y $的有界线性运算符。该方法中使用了强凸的惩罚函数，以选择具有所需功能的解决方案。在寻求解决方案的各种源条件下，当方法通过{\ it先验}停止规则或差异原理终止该方法时，会得出收敛速率。我们还考虑了该方法及其各种应用的加速度。
In this paper we consider a dual gradient method for solving linear ill-posed problems $Ax = y$, where $A : X \to Y$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y$. A strongly convex penalty function is used in the method to select a solution with desired feature. Under variational source conditions on the sought solution, convergence rates are derived when the method is terminated by either an {\it a priori} stopping rule or the discrepancy principle. We also consider an acceleration of the method as well as its various applications.
