We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the generated sequences converge to a critical point of the objective function, if a regularization of the objective function satisfies the Kurdyka-{\L}ojasiewicz property. Further, we provide convergence rates for the generated sequences and the function values formulated in terms of the {\L}ojasiewicz exponent.

中文翻译：

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与平滑非凸最小化相关的梯度类型惯性算法的收敛率

我们研究了一种与非凸可微函数的最小化相关的梯度类型惯性算法。该算法是根据 Nesterov 的加速凸梯度方法的精神制定的。我们表明，如果目标函数的正则化满足 Kurdyka-{\L}ojasiewicz 属性，则生成的序列会收敛到目标函数的临界点。此外，我们提供了生成序列的收敛速度和根据 {\L}ojasiewicz 指数公式化的函数值。