An accelerated proximal augmented Lagrangian method and its application in compressive sensing

• Main Authors: Min Sun, Jing Liu
• Format: Article
• Language: English
• Published: SpringerOpen 2017-10-01
• Series: Journal of Inequalities and Applications
• Subjects: proximal augmented Lagrangian multiplier method; convex programming; global convergence; compressive sensing
• Online Access: http://link.springer.com/article/10.1186/s13660-017-1539-0

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.