轨道仿射包上的拟非扩张迭代：从Mann均值算法到惯性方法
Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods
摘要：
不动点迭代在大量优化算法的设计和分析中起着核心作用。我们研究了一种新的迭代格式，其中的更新是通过将拟非扩张算子的组合应用于到当前点生成的轨道的仿射包中的一个点来获得的。这项调查统一了几个算法结构，包括曼的平均值方法，惯性方法，和多层无记忆方法。它还提供了一个框架，为发展新的算法，如我们提出的解决单调包含和最小化问题。
英文摘要：
Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multi-layer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems.
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