论文标题
一种相对错误的惯性 - 利用不截止性的投影分裂算法
A relative-error inertial-relaxed inexact projective splitting algorithm
论文作者
论文摘要
为了解决涉及许多最大单调算子总和的结构化单调包含问题，我们提出并研究了相对异常的惯性 - 释放不删除的不切度不切实际的投影型分裂算法。所提出的算法受益于惯性和放松效应的组合，这两者都由一定范围内的参数控制。我们对这些参数提出了足够的条件，并研究了它们之间的相互作用，以确保算法产生的序列的弱收敛性。另外，所提出的算法还受益于相对纠正标准中不精确的子问题解决方案。与以前的（非允许和精确）版本的投射拆分相比，有关套索问题的说明性数值实验表明有所改善。
For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters and study the interplay between them in order to guarantee weak convergence of sequences generated by our algorithm. Additionally, the proposed algorithm also benefits from inexact subproblem solution within a relative-error criterion. Illustrative numerical experiments on LASSO problems indicate some improvement when compared with previous (noninertial and exact) versions of projective splitting.
