论文标题
向前反复反复反复反复的分裂方法的强烈收敛，用于求解单调包含物，并应用图像恢复和最佳控制
Strong Convergence of Forward-Reflected-Backward Splitting Methods for Solving Monotone Inclusions with Applications to Image Restoration and Optimal Control
论文作者
论文摘要
在本文中，我们提出并研究了Malitsky和TAM的前反向回形分裂方法的几种强烈收敛版本，以在真正的Hilbert空间中找到两个单调算子的总和中的零。我们提出的方法只需要对单价操作员进行一次前瞻性评估，并需要对每次迭代的设置值运算符进行一个向后评估。文献中许多其他可用的强烈收敛分裂方法中缺乏的功能。我们还开发了方法的惯性版本，当设置值运算符是最大单调的，而单值操作员是Lipschitz的连续和单调时，这些方法将获得这些方法的强收敛结果。最后，与文献中的已知相关方法相比，我们讨论了图像修复和最佳控制中的一些示例。
In this paper, we propose and study several strongly convergent versions of the forward-reflected-backward splitting method of Malitsky and Tam for finding a zero of the sum of two monotone operators in a real Hilbert space. Our proposed methods only require one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. We also develop inertial versions of our methods and strong convergence results are obtained for these methods when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous and monotone. Finally, we discuss some examples from image restorations and optimal control regarding the implementations of our methods in comparison with known related methods in the literature.
