Improved proximal ADMM with partially parallel splitting for multi-block separable convex programming

For a type of multi-block separable convex programming raised in machine learning and statistical inference, we propose a proximal alternating direction method of multiplier (PADMM) with partially parallel splitting, which has the following nice properties: (1) To alleviate the weight of the proximal terms, the restrictions imposed on the proximal parameters are relaxed substantively; (2) … Read more

Proximal ADMM with larger step size for two-block separable convex programs

The alternating direction method of multipliers (ADMM) is a benchmark for solving two-block separable convex programs, and it finds more and more applications in many areas. However, as other first-order methods, ADMM also suffers from low convergence. In this paper, to accelerate the convergence of ADMM, we relax the restriction region of the Fortin and … Read more

The symmetric ADMM with positive-indefinite proximal regularization and its application

Due to update the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practice, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often … Read more