Deterministic and randomized, row-action and column-action solvers have become increasingly popular owing to their simplicity, low computational and memory complexities, and ease of composition with other techniques. Indeed, such solvers can be highly tailored to the given problem structure and to the hardware platform on which the problem will be solved. However, whether such tailored solvers will converge to a solution is unclear. In this work, we provide a general set of assumptions under which such solvers are guaranteed to converge with probability one. As a result, we can provide practitioners with guidance on how to design highly tailored solvers that are also guaranteed to converge.
翻译：由于其简单、计算和记忆复杂程度低、与其他技术的构成容易,确定性、随机、行动作和分队动作的解决方案越来越受欢迎。 事实上,这些解决方案可以高度适应特定问题结构和解决问题的硬件平台。 然而,这些定制的解决方案是否会趋同于解决方案尚不清楚。 在这项工作中,我们提供了一套一般假设,保证这些解决方案与概率一趋同。因此,我们可以为从业人员提供如何设计高度定制的解决方案的指导,这些解决方案也得到保证会趋同。
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