A New Sequential Updating Scheme of the Lagrange Multiplier for Multi-Block Linearly Constrained Separable Convex Optimization with Relaxed Step Sizes

In various applications such as signal/image processing, data mining, statistical learning and etc., the multi-block linearly constrained separable convex optimization is frequently used, where the objective function is the sum of multiple individual convex functions, and the major constraints are linear. A classical method for solving such kind of optimization problem could be the alternating … Read more

A Partial PPA block-wise ADMM for Multi-Block Constrained Separable Convex Optimization

The alternating direction method of multipliers(ADMM) has been proved to be effective for solving two-block separable convex optimization subject to linear constraints. However, it is not necessarily convergent when it is extended to multiple-block case directly. One remedy could be regrouping multiple-block variables into two groups firstly and then adopting the classic ADMM to the … Read more

A One-Parameter Family of Middle Proximal ADMM for Constrained Separable Convex Optimization

This work is devoted to studying a family of Middle Proximal Alternating Direction Method of Multipliers (MP-ADM) for solving multi-block constrained separable convex optimization. Such one-parameter family of MP-ADM combines both Jacobian and Gauss-Seidel types of alternating direction method, and proximal point techniques are only applied to the middle subproblems to promote the convergence. We … Read more