A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
A Logarithmic-Quadratic Proximal Method for Variational Inequalities
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Convergence of Proximal-Like Algorithms
SIAM Journal on Optimization
Computers & Mathematics with Applications
TILT: Transform Invariant Low-Rank Textures
International Journal of Computer Vision
Computational Optimization and Applications
An ADM-based splitting method for separable convex programming
Computational Optimization and Applications
A proximal parallel splitting method for minimizing sum of convex functions with linear constraints
Journal of Computational and Applied Mathematics
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The typical structured variational inequalities can be interpreted as a system of equilibrium problems with a leader and two cooperative followers. Assume that, based on the instruction given by the leader, each follower can solve the individual equilibrium sub-problems in his own way. The responsibility of the leader is to give a more reasonable instruction for the next iteration loop based on the feedback information from the followers. This consideration leads us to present a parallel splitting augmented Lagrangian method (abbreviated to PSALM). The proposed method can be extended to solve the system of equilibrium problems with three separable operators. Finally, it is explained why we cannot use the same technique to develop similar methods for problems with more than three separable operators.