Perturbed proximal primal–dual algorithm for nonconvex nonsmooth optimization
Perturbed proximal primal–dual algorithm for nonconvex nonsmooth optimization
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DOI：
10.1007/s10107-019-01365-4
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发表时间：
2019-02
影响因子：
2.7
通讯作者：
Davood Hajinezhad;Mingyi Hong
中科院分区：
文献类型：
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作者：
Davood Hajinezhad;Mingyi Hong
本文针对一类重要的线性约束优化问题，提出了一种摄动近端原始对偶算法（PProx-PDA），该算法的目标是光滑（可能非凸）和凸（可能非光滑）函数的和。这类问题可用于许多统计和工程应用的建模，如高维子空间估计和分布式机器学习。所提出的方法是Uzawa型，其中执行一个原始梯度下降步骤，然后执行一个（近似）双梯度上升步骤。该算法的一个显著特征是使用过去的迭代对原步和对偶步都进行了适当的扰动，从而可以获得一些渐近收敛和收敛速度的结果（到一阶平稳解）。最后，我们进行了大量的数值实验来验证所提出算法的有效性。
In this paper, we propose a perturbed proximal primal–dual algorithm (PProx-PDA) for an important class of linearly constrained optimization problems, whose objective is the sum of smooth (possibly nonconvex) and convex (possibly nonsmooth) functions. This family of problems can be used to model many statistical and engineering applications, such as high-dimensional subspace estimation and the distributed machine learning. The proposed method is of the Uzawa type, in which a primal gradient descent step is performed followed by an (approximate) dual gradient ascent step. One distinctive feature of the proposed algorithm is that the primal and dual steps are both perturbed appropriately using past iterates so that a number of asymptotic convergence and rate of convergence results (to first-order stationary solutions) can be obtained. Finally, we conduct extensive numerical experiments to validate the effectiveness of the proposed algorithm.