论文标题
一种用于最小提升的复合单调夹杂物的原始二重分裂算法
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting
论文作者
论文摘要
在这项工作中，我们研究了解决复合单调包含问题的分解分解算法。这些一般问题的目的是在由线性操作员组成的最大单调操作员的总和中找到零。我们的主要贡献是建立第一种原始二重分裂算法，用于最小提升的复合单调夹杂物。具体而言，所提出的方案缩小了与其他算法相比，定义了基础固定点运算符的产品空间的尺寸，而无需对分辨率运算符进行其他评估。我们证明了这种新算法的收敛性，并在图像去蓝和变性中分析了其性能。这项工作还通过扩展了Malitsky和TAM对具有分解参数的方案最近证明的最小提升定理，从而有助于解决分解算法的理论。
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting. Specifically, the proposed scheme reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators. We prove the convergence of this new algorithm and analyze its performance in a problem arising in image deblurring and denoising. This work also contributes to the theory of resolvent splitting algorithms by extending the minimal lifting theorem recently proved by Malitsky and Tam to schemes with resolvent parameters.
