We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems.

中文翻译：

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近邻方法避免了弱凸函数的有效严格鞍形

我们为非光滑函数引入了几何透明的严格鞍形属性。此属性确保在随机初始化时，针对弱凸问题的简单近端算法仅收敛到局部极小值。我们认为严格的鞍属性在应用中可能是一个现实的假设，因为它可证明适用于一般的半代数优化问题。