论文标题
刀具引起的常见固定点问题的广义基础投影方法
A Generalized Block-Iterative Projection Method for the Common Fixed Point Problem Induced by Cutters
论文作者
论文摘要
Aharoni和Censor的块词（BIP）方法[块状投影方法，用于平行计算解决可行性问题的解决方案，线性代数及其应用120，（1989），165--175]是一个迭代过程，是一个迭代的过程，无法在无空中寻找无空的综合体。它在使用操作员的“块”算法方面对单个子集进行了正交投影，并且在构建特定算法方面具有极大的灵活性。我们扩展了这种算法方案，以处理连续切割器操作员的家族，并找到其共同的固定点。由于连续切割器的家族包括几个重要的特定操作员，因此我们的广义方案确保了全球融合并保留BIP的灵活性，尤其是指标（正交）投影仪和连续的亚级别预测，这在应用中非常重要。我们还允许包括某种自适应扰动，并在途中，我们得出了具有独立利益的扰动Fejér单调性引理。
The block-iterative projections (BIP) method of Aharoni and Censor [Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, Linear Algebra and its Applications 120, (1989), 165--175] is an iterative process for finding asymptotically a point in the nonempty intersection of a family of closed convex subsets. It employs orthogonal projections onto the individual subsets in an algorithmic regime that uses "blocks" of operators and has great flexibility in constructing specific algorithms from it. We extend this algorithmic scheme to handle a family of continuous cutter operators and to find a common fixed point of them. Since the family of continuous cutters includes several important specific operators, our generalized scheme, which ensures global convergence and retains the flexibility of BIP, can handle, in particular, metric (orthogonal) projectors and continuous subgradient projections, which are very important in applications. We also allow a certain kind of adaptive perturbations to be included, and along the way we derive a perturbed Fejér monotonicity lemma which is of independent interest.
