We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain $[0,1]^2$ is PPAD $\cap$ PLS-complete. This is the first non-artificial problem to be shown complete for this class. Our results also imply that the class CLS (Continuous Local Search) - which was defined by Daskalakis and Papadimitriou as a more "natural" counterpart to PPAD $\cap$ PLS and contains many interesting problems - is itself equal to PPAD $\cap$ PLS.

翻译：我们研究通过在一条交界的锥形多端形域上执行渐渐下潜线可以解决的搜索问题, 并显示该类与两大已知类别( PPAD 和 PLS ) 的交叉点相等。 作为我们的主要基本技术贡献, 我们证明计算一个在域上持续不同功能的Karush- Kuhn- Tucker (KKT) 点($0, 1,2美元) 是完成该类的PPAD $\ cap$ PLS 的第一个非人工问题。 我们的结果还表明, 由 Daskalakis 和 Papadimitriou 定义的CLS (持续本地搜索) 类( 由 Daskalakis 和 Papadimitriou ) 类( 由 PPADD$\ cap$ PLS 定义的更“ 自然” 对应点, 包含许多有趣的问题) 本身等于 PPPAD$ cap$ PLS 。</s>