iPiano: Inertial Proximal Algorithm for Nonconvex Optimization
iPiano: Inertial Proximal Algorithm for Nonconvex Optimization
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DOI：
10.1137/130942954
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发表时间：
2014-01-01
影响因子：
2.1
通讯作者：
Pock, Thomas
中科院分区：
文献类型：
--
作者：
Ochs, Peter;Chen, Yunjin;Pock, Thomas
本文研究了一种求解由可微（可能非凸）函数和凸（可能不可微）函数组成的最小化问题的算法。iPiano算法将前后分裂与惯性力相结合。它可以被看作是Polyak的Heavy-ball方法的非光滑分裂版本。对所提出的一类问题的算法进行了严格的分析，得到了函数值和参数的全局收敛性。这使得该算法在非凸问题上的使用具有鲁棒性。利用Kurdyka-Lojasiewicz不等式得到了收敛性结果。这是一个非常弱的限制，用于证明其他几种梯度方法的收敛性。首先证明了遗传算法的一个抽象收敛定理，然后证明了iPiano算法满足该定理的要求。此外，收敛速度建立一般问题类。我们展示了iPiano在计算机视觉问题上的应用-使用学习先验的图像去噪和基于扩散的图像压缩。
In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a nonsmooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on nonconvex problems. The convergence result is obtained based on the Kurdyka-Lojasiewicz inequality. This is a very weak restriction, which was used to prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic algorithm is proved, and then iPiano is shown to satisfy the requirements of this theorem. Furthermore, a convergence rate is established for the general problem class. We demonstrate iPiano on computer vision problems-image denoising with learned priors and diffusion based image compression.