SIAM Journal on Optimization, Volume 31, Issue 3, Page 1877-1896, January 2021.
We consider a nonconvex optimization problem consisting of maximizing the difference of two convex functions. We present a randomized method that requires low computational effort at each iteration. The described method is a randomized coordinate descent method employed on the so-called Toland-dual problem. We prove subsequence convergence to dual stationarity points, a new notion that we introduce and which is shown to be tighter than standard criticality. An almost sure rate of convergence of an optimality measure of the dual sequence is proven. We demonstrate the potential of our results on three principal component analysis models resulting in extremely simple algorithms.

中文翻译：

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求解一类非凸问题的对偶随机坐标下降法

SIAM Journal on Optimization，第 31 卷，第 3 期，第 1877-1896 页，2021 年 1 月。
我们考虑一个非凸优化问题，包括最大化两个凸函数的差异。我们提出了一种随机方法，每次迭代都需要较少的计算量。所描述的方法是在所谓的托兰德对偶问题上采用的随机坐标下降法。我们证明了对双平稳点的子序列收敛，这是我们引入的一个新概念，它被证明比标准临界性更严格。证明了对偶序列的最优性度量的几乎确定的收敛速度。我们展示了我们的结果在三个主成分分析模型上的潜力，从而产生了极其简单的算法。