We consider the problem of minimization for a function with Lipschitz continuous gradient on a proximally smooth and smooth manifold in a finite dimensional Euclidean space. We consider the Lezanski-Polyak-Lojasiewicz (LPL) conditions in this problem of constrained optimization. We prove that the gradient projection algorithm for the problem converges with a linear rate when the LPL condition holds.

中文翻译：

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非凸情况下光滑集和函数的梯度投影算法

我们考虑在有限维欧几里得空间中的近端平滑流形上具有Lipschitz连续梯度的函数的最小化问题。在此约束优化问题中，我们考虑了Lezanski-Polyak-Lojasiewicz（LPL）条件。我们证明了当LPL条件成立时，该问题的梯度投影算法以线性速率收敛。