In this paper, we put forth a novel framework (named ``RYU'') for the construction of ``safe'' balls, i.e. regions that provably contain the dual solution of a target optimization problem. We concentrate on the standard setup where the cost function is the sum of two terms: a closed, proper, convex Lipschitz-smooth function and a closed, proper, convex function. The RYU framework is shown to generalize or improve upon all the results proposed in the last decade for the considered family of optimization problems.

翻译：本文提出了一种新型框架（命名为“RYU”），用于构建“安全”球，即能够确定目标优化问题对偶解的包含区域。我们聚焦于标准设置，其中代价函数由两项之和构成：一个闭真凸Lipschitz光滑函数与一个闭真凸函数。研究表明，RYU框架能够推广或改进过去十年间针对此类优化问题家族所提出的所有现有成果。