论文标题
具有不同惯性术语的前向后算法，用于结构化的非凸极小问题
Forward-backward algorithms with different inertial terms for structured non-convex minimization problems
论文作者
论文摘要
我们研究了两种惯性前向算法，与非平滑和可能的非凸的总和和非凸线可区分函数相关的最小化。该算法是本着著名的Fista方法的精神制定的，但是设置是非凸的，我们允许不同的惯性术语。此外，我们算法中的惯性参数也可以占负值。当非平滑函数是凸的时，我们还可以对待情况，并且在这种情况下，我们可以允许更好的步长。我们证明了一些应用于我们的数值方案的抽象收敛结果，使我们能够证明生成的序列会收敛到目标函数的临界点，前提是目标函数的正则化满足Kurdyka-lojasiewicz属性。此外，我们获得了应用于我们的数值方案的一般结果，可确保生成序列的收敛速率以及根据目标函数正规化的KL指数提出的目标函数值。最后，我们将结果应用于图像恢复。
We investigate two inertial forward-backward algorithms in connection with the minimization of the sum of a non-smooth and possibly non-convex and a non-convex differentiable function. The algorithms are formulated in the spirit of the famous FISTA method, however the setting is non-convex and we allow different inertial terms. Moreover, the inertial parameters in our algorithms can take negative values too. We also treat the case when the non-smooth function is convex and we show that in this case a better step size can be allowed. We prove some abstract convergence results which applied to our numerical schemes allow us to show that the generated sequences converge to a critical point of the objective function, provided a regularization of the objective function satisfies the Kurdyka-Lojasiewicz property. Further, we obtain a general result that applied to our numerical schemes ensures convergence rates for the generated sequences and for the objective function values formulated in terms of the KL exponent of a regularization of the objective function. Finally, we apply our results to image restoration.
