论文标题
关于DCA的收敛分析
On the convergence analysis of DCA
论文作者
论文摘要
在本文中，我们提出了一个干净而通用的证明框架，以建立标准DC程序和凸面限制的DC程序的差差（DC）编程算法（DCA）的收敛分析。我们首先讨论有关DCA确定性的合适假设。然后，我们专注于DCA的收敛分析，尤其是DCA在Lojasiewicz子级别不平等和Kurdyka-lojasiewicz属性下生成的序列$ \ {X^K \} $的全局收敛性。此外，还研究了序列$ \ {f（x^k）\} $和$ \ {\ | x^k-x^*\ | \} $的收敛速率。我们希望本文介绍的证明框架将是一个有用的工具，可以方便地为DCA和新的DCA型算法的许多变体建立收敛分析。
In this paper, we propose a clean and general proof framework to establish the convergence analysis of the Difference-of-Convex (DC) programming algorithm (DCA) for both standard DC program and convex constrained DC program. We first discuss suitable assumptions for the well-definiteness of DCA. Then, we focus on the convergence analysis of DCA, in particular, the global convergence of the sequence $\{x^k\}$ generated by DCA under the Lojasiewicz subgradient inequality and the Kurdyka-Lojasiewicz property respectively. Moreover, the convergence rate for the sequences $\{f(x^k)\}$ and $\{\|x^k-x^*\|\}$ are also investigated. We hope that the proof framework presented in this article will be a useful tool to conveniently establish the convergence analysis for many variants of DCA and new DCA-type algorithms.
