论文标题
通过块更新解决复合固定点问题
Solving Composite Fixed Point Problems with Block Updates
论文作者
论文摘要
可以通过在每次迭代时仅激活一个操作员，可以使用各种策略来迭代迭代的迭代固定点。在涉及不共享共同固定点的操作员的一系列更具挑战性的复合固定点问题中，当前方法需要在每次迭代中激活所有操作员，以及在仅更新操作员块的同时保持收敛的问题。我们提出了一种实现此目标并分析其渐近行为的方法。通过利用与集中阵列理论的联系来确定弱，强和线性收敛结果。提出了几个非线性和非平滑分析问题的应用，从单调包含物和不一致的可行性问题到最小化数据科学中出现的问题。
Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators that do not share common fixed points, current methods require the activation of all the operators at each iteration, and the question of maintaining convergence while updating only blocks of operators is open. We propose a method that achieves this goal and analyze its asymptotic behavior. Weak, strong, and linear convergence results are established by exploiting a connection with the theory of concentrating arrays. Applications to several nonlinear and nonsmooth analysis problems are presented, ranging from monotone inclusions and inconsistent feasibility problems, to minimization problems arising in data science.
