论文标题
外部反射前后拆分算法用于求解单调包含物
An outer reflected forward-backward splitting algorithm for solving monotone inclusions
论文作者
论文摘要
单调夹杂物在解决信号和图像处理，机器学习和医疗图像重建中产生的各种凸优化问题方面具有广泛的应用。在本文中，我们提出了一种新的分裂算法，以查找最大单调操作员的总和的零，单调Lipschitzian操作员和一个可核操作员，该操作员称为外部反射向前反复反复的分裂算法。在迭代参数的轻度条件下，我们证明了所提出的算法的收敛性。作为应用，我们采用了提出的算法来求解涉及单调Lipschitzian操作员，Cocoercive Operator的复合单调夹杂物和操作员的平行总和。获得的算法的优点是它是一种完全分裂的算法，在该算法中，Lipschitzian运算符和cocoercive操作员是通过明确的步骤处理的，并且通过其分辨率处理了最大的单调操作员。
Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for finding a zero of the sum of a maximally monotone operator, a monotone Lipschitzian operator, and a cocoercive operator, which is called outer reflected forward-backward splitting algorithm. Under mild conditions on the iterative parameters, we prove the convergence of the proposed algorithm. As applications, we employ the proposed algorithm to solve composite monotone inclusions involving monotone Lipschitzian operator, cocoercive operator, and the parallel sum of operators. The advantage of the obtained algorithm is that it is a completely splitting algorithm, in which the Lipschitzian operator and the cocoercive operator are processed via explicit steps and the maximally monotone operators are processed via their resolvents.
