An inexact ADMM with proximal-indefinite term and larger stepsize

This work is devoted to developing an inexact ADMM for solving a family of multi-block separable convex optimization problems subject to linear equality constraints, where the problem variables are artificially partitioned into two groups. The first grouped subproblems are solved inexactly and and parallelly under relative error criterions, while the second grouped single subproblem (often … Read more

Solution to a Monotone Inclusion Problem using the Relaxed Peaceman-Rachford Splitting Method: Convergence and its Rates

We consider the convergence behavior using the relaxed Peaceman-Rachford splitting method to solve the monotone inclusion problem $0 \in (A + B)(u)$, where $A, B: \Re^n \rightrightarrows \Re^n$ are maximal $\beta$-strongly monotone operators, $n \geq 1$ and $\beta > 0$. Under a technical assumption, convergence of iterates using the method on the problem is proved … Read more