首页|A Balanced Augmented Lagrangian Method with Correction for Linearly Constrained Optimization
A Balanced Augmented Lagrangian Method with Correction for Linearly Constrained Optimization
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NETL
NSTL
Springer Nature
Abstract 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 (He and Yuan, arXiv, 2021) by transferring some computational workloads from the augmented subproblem to the Lagrange multiplier. In this paper, 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 under some mild conditions. 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.
NETL
NSTL
Springer Nature
