In this paper, we develop an Inexact Relaxed Augmented Lagrangian Method (IR-ALM) for solving a class of convex optimization problems. Flexible relative error criteria are designed for approximately solving the resulting subproblem, and a relaxation step is exploited to accelerate its convergence numerically. By a unified variational analysis, we establish the global convergence of this IR-ALM and its sublinear convergence rate in terms of the primal iterative residual, the objective function value gap and constraint violation, respectively. Experimental results on testing the image restoration problem with different types of images show that the proposed method is effective.
Citation
J. Bai, Y. Chen, Y.Ma, Convergence analysis of an inexact relaxed augmented Lagrangian method, Pacific Journal of Optimization, https://doi.org/10.61208/pjo-2024-019，(2024)
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