In this paper, we present a new framework, called "RYU" for constructing "safe" regions -- specifically, bounded sets that are guaranteed to contain the dual solution of a target optimization problem. Our framework applies to the standard case where the objective function is composed of two components: a closed, proper, convex function with Lipschitz-smooth gradient and another closed, proper, convex function. We show that the RYU framework not only encompasses but also improves upon the state-of-the-art methods proposed over the past decade for this class of optimization problems.

翻译：本文提出了一种称为"RYU"的新框架，用于构建"安全"区域——具体而言，即保证包含目标优化问题对偶解的有界集合。本框架适用于目标函数由两个分量组成的标准情形：一个具有Lipschitz光滑梯度的闭、真、凸函数，以及另一个闭、真、凸函数。我们证明RYU框架不仅涵盖了近十年来针对此类优化问题提出的最先进方法，而且对其进行了改进。