A balanced augmented Lagrangian method with correction for linearly constrained optimization

报告摘要：Augmented Lagrangian method (ALM) is a quintessential prototype for linearly constrained optimization. However, a crude use of ALM is rarely possible due to the challenging augmented subproblem. A balanced ALM was recently innovated by transferring some computational workloads from the augmented subproblem to the Lagrange multiplier. In this talk, by deploying the prediction-correction framework, we further ameliorate the balanced ALM by introducing a correction step. The O(1/N) convergence rates of the proposed method in both ergodic and nonergodic senses are established. With the perspectives of spectral decomposition, we analyze the coefficients involving convergence rate of the proposed method. Numerical simulations on some image recovery problems demonstrate the compelling performance of the proposed method.

报告人简介：张文星，电子科技大学数学科学学院，硕士导师，2012年于南京大学数学系获博士学位。曾于法国图卢兹大学、香港浸会大学等高校从事博士后/访问交流。中国运筹学会数学规划分会青年理事。中国运筹学会算法软件与应用分会常务理事。研究兴趣为变分不等式理论、算法及应用。四川省学术和技术带头人后备人选。在Math Comput, Inverse Problems, SIAM J Imaging Sci, J Sci Comput, IEEE系列杂志发表论文多篇。