The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical fast convergence rate under weak conditions. However, for problems such as X-ray computed tomography (CT) image reconstruction and large-scale sparse regression with "big data", where there is no efficient way to solve the inner least-squares problem, the AL method can be slow due to the inevitable iterative inner updates. In this paper, we focus on solving regularized (weighted) least-squares problems using a linearized variant of the AL method that replaces the quadratic AL penalty term in the scaled augmented Lagrangian with its separable quadratic surrogate (SQS) function, thus leading to a much simpler ordered-subsets (OS) accelerable splitting-based algorithm, OS-LALM, for X-ray CT image reconstruction. To further accelerate the proposed algorithm, we use a second-order recursive system analysis to design a deterministic downward continuation approach that avoids tedious parameter tuning and provides fast convergence. Experimental results show that the proposed algorithm significantly accelerates the "convergence" of X-ray CT image reconstruction with negligible overhead and greatly reduces the OS artifacts in the reconstructed image when using many subsets for OS acceleration.
P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution
Department of Industrial & Systems Engineering, The University of Tennessee, Knoxville, TN, USA（工业与系统工程系，田纳西大学， Knoxville，TN，美国）；Charles F. Dolan School of Business, Fairfield University, Fairfield, USA（查尔斯·F·多兰商学院，费尔菲尔德大学， Fairfield，美国）；Department of Electrical Engineering & Computer Science, The University of Tennessee, Knoxville, TN, USA（电气工程与计算机科学系，田纳西大学， Knoxville，TN，美国）
A Fixed-Penalty Linearized Augmented Lagrangian Method with Classical Multiplier Updates
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；College of Science, National University of Defense Technology（国防科技大学理学院）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）
Restarted Reflected Halpern Acceleration for Augmented Primal-Dual Methods
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Alibaba US, DAMO Academy（阿里巴巴美国达摩院）
