Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
A variable-penalty alternating directions method for convex optimization
Mathematical Programming: Series A and B
Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities
SIAM Journal on Optimization
Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities
Computational Optimization and Applications
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
A Parallel Splitting Method for Coupled Monotone Inclusions
SIAM Journal on Control and Optimization
Multidimensional Systems and Signal Processing
SIAM Journal on Scientific Computing
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
SIAM Journal on Optimization
Some projection methods with the BB step sizes for variational inequalities
Journal of Computational and Applied Mathematics
Alternating Direction Method for Covariance Selection Models
Journal of Scientific Computing
Hi-index | 7.29 |
In this paper, we propose a proximal parallel decomposition algorithm for solving the optimization problems where the objective function is the sum of m separable functions (i.e., they have no crossed variables), and the constraint set is the intersection of Cartesian products of some simple sets and a linear manifold. The m subproblems are solved simultaneously per iterations, which are sum of the decomposed subproblems of the augmented Lagrange function and a quadratic term. Hence our algorithm is named as the 'proximal parallel splitting method'. We prove the global convergence of the proposed algorithm under some mild conditions that the underlying functions are convex and the solution set is nonempty. To make the subproblems easier, some linearized versions of the proposed algorithm are also presented, together with their global convergence analysis. Finally, some preliminary numerical results are reported to support the efficiency of the new algorithms.