论文标题
镜子惯性向前反向反复反复的拆分：全球收敛和线路搜索扩展超出了凸平和lipschitz的光滑度
A mirror inertial forward-reflected-backward splitting: Global convergence and linesearch extension beyond convexity and Lipschitz smoothness
论文作者
论文摘要
这项工作调查了前反向回复算法的Bregman和惯性扩展[Y. Malitsky和M. Tam，Siam J. Optim。，30（2020），pp。1451--1472]应用于相对平滑度下的结构化非凸最小化问题。为此，所提出的算法取决于两个关键特征：在双重空间中采取惯性步骤，并允许可能负面惯性值。我们的分析始于研究相关的包络函数，该功能通过新颖的产品空间公式考虑了惯性术语。这种结构与文献中的类似对象有很大不同，可以为扩展分裂算法提供新的见解。全球收敛和利率是通过吸引广义凹库伊斯维奇（KLDONKA-LOJASIEWICZ（KL）的属性来获得的，这使我们能够描述迭代率的急剧上限。最后，给出了线路搜索扩展，以增强提出的方法。
This work investigates a Bregman and inertial extension of the forward-reflected-backward algorithm [Y. Malitsky and M. Tam, SIAM J. Optim., 30 (2020), pp. 1451--1472] applied to structured nonconvex minimization problems under relative smoothness. To this end, the proposed algorithm hinges on two key features: taking inertial steps in the dual space, and allowing for possibly negative inertial values. Our analysis begins with studying an associated envelope function that takes inertial terms into account through a novel product space formulation. Such construction substantially differs from similar objects in the literature and could offer new insights for extensions of splitting algorithms. Global convergence and rates are obtained by appealing to the generalized concave Kurdyka-Lojasiewicz (KL) property, which allows us to describe a sharp upper bound on the total length of iterates. Finally, a linesearch extension is given to enhance the proposed method.
