SIAM Journal on Optimization, Volume 30, Issue 2, Page 1391-1420, January 2020.
We study inertial versions of primal-dual proximal splitting, also known as the Chambolle--Pock method. Our starting point is the preconditioned proximal point formulation of this method. By adding correctors corresponding to the antisymmetric part of the relevant monotone operator, using a FISTA-style gap unrolling argument, we are able to derive gap estimates instead of merely ergodic gap estimates. Moreover, based on adding a diagonal component to this corrector, we are able to combine strong convexity based acceleration with inertial acceleration. We test our proposed method on image processing and inverse problems, obtaining convergence improvements for sparse Fourier inversion and positron emission tomography.

中文翻译：

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惯性，修正，原始对偶近端分裂

SIAM优化杂志，第30卷，第2期，第1391-1420页，2020年1月。
我们研究原始-对偶近端分裂的惯性形式，也称为Chambolle-Pock方法。我们的出发点是该方法的预处理近端点公式。通过使用FISTA样式的间隙展开参数，添加与相关单调算符的反对称部分相对应的校正器，我们能够得出间隙估计值，而不仅仅是遍历遍历的间隙估计值。此外，基于向该校正器添加对角线分量，我们能够将基于强凸度的加速度与惯性加速度相结合。我们在图像处理和反问题上测试了我们提出的方法，获得了稀疏傅里叶反演和正电子发射断层扫描的收敛性改进。