An accelerated proximal augmented Lagrangian method and its application in compressive sensing - Min Sun; Jing Liu (Journal of Inequalities and Applications, 2017)
Abstract As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable’s subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case O ( 1 / t 2 ) $\mathcal{O}(1/t^{2})$ convergence rate of PALM-IPR in a non-ergodic sense. Finally, numerical results show that our new method is feasible and efficient for solving compressive sensing.