This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose novel near-optimal methods for smooth and nonsmooth problems by reformulating them into functionally constrained problems.

翻译：本文研究简单双层问题，其中凸上层函数在凸下层问题的最优解集上最小化。我们首先证明简单双层问题的根本困难在于：此类问题的近似最优值无法通过一阶零保持算法获得。随后我们遵循近期研究思路，寻求弱近似解。为此目标，我们通过将光滑与非光滑问题重构为功能约束问题，提出了新型近最优算法。