论文标题
一种环状反射方法，用于查找牢固的非专业操作员的常见固定点
A circumcentered-reflection method for finding common fixed points of firmly nonexpansive operators
论文作者
论文摘要
最近提出了周围的反射方法（CRM）作为加速几种算法来解决凸的可行性问题（CFP）的方法，相当于在有限数量的封闭数量和凸面集上找到正交投影的共同定点。在本文中，我们将CRM应用于更通用的固定点问题（称为FPP），包括找到属于较大运营商家族的常见运算符的常见固定点，即坚定的非专业操作员。我们证明了比在这种情况下，CRM在全球范围内收敛到一个共同的固定点（假设至少存在一个）。我们还建立了在不太苛刻的误差绑定假设下，由CRM应用于FPP产生的序列的线性收敛，并提供了渐近常数的估计。与经典平行投影方法（PPM）相比，我们提供了CRM优势的可靠数值证据。此外，我们还提出了正交预测的凸组合的某些结果，这本身就是一种兴趣。
The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal projections onto a finite number of closed and convex sets. In this paper, we apply CRM to the more general Fixed Point Problem (denoted as FPP), consisting of finding a common fixed-point of operators belonging to a larger family of operators, namely firmly nonexpansive operators. We prove than in this setting, CRM is globally convergent to a common fixed-point (supposing at least one exists). We also establish linear convergence of the sequence generated by CRM applied to FPP, under a not too demanding error bound assumption, and provide an estimate of the asymptotic constant. We provide solid numerical evidence of the superiority of CRM when compared to the classical Parallel Projections Method (PPM). Additionally, we present certain results of convex combination of orthogonal projections, of some interest on its own.
