Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems
Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems
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DOI：
10.1137/16m1064064
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发表时间：
2016-01-01
影响因子：
2.1
通讯作者：
Sabach, Shoham
中科院分区：
文献类型：
--
作者：
Pock, Thomas;Sabach, Shoham
在本文中，我们研究了非凸和非平滑的优化问题，该问题与半格言数据一起研究，其中变量向量分为几个变量块。该问题由整个变量向量的一个平滑函数和每个块的非平滑函数总和组成。我们分析了近端交替线性化最小化算法的惯性版本，并证明了其全局收敛到手头目标函数的临界点。我们通过在盲图片反卷积，稀疏的非负矩阵分解和字典学习上介绍数值实验来说明我们的理论发现，这证明了所提出方法的可行性和有效性。
In this paper we study nonconvex and nonsmooth optimization problems with semialgebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector and the sum of nonsmooth functions for each block separately. We analyze an inertial version of the proximal alternating linearized minimization algorithm and prove its global convergence to a critical point of the objective function at hand. We illustrate our theoretical findings by presenting numerical experiments on blind image deconvolution, on sparse nonnegative matrix factorization and on dictionary learning, which demonstrate the viability and effectiveness of the proposed method.