We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than that of linearized ADMM, in...

ii APPROVAL of a dissertation submitted by Nicomedes Alonso III This dissertation has been read by each member of the dissertation committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the MSU Division of Graduate Education. In presenting this dissertation in partial fulfillment o...

We introduce an accurate and efficient alternating-direction method for solving a viscous wave equation which is based on a three-level, second-order correct implicit algorithm and which has a splitting error not significantly larger than the truncation error of the base method.

Recently the alternating direction method of multipliers (ADMM) has been widely used for various applications arising in scientific computing areas. Most of these application models are, or can be easily reformulated as, linearly constrained convex minimization models with separable nonlinear objective functions. In this note we show that ADMM can also be easily used for the canonical linear pr...

1. The strongly convex case 1.1. Proof of Lemma 1 Lemma 1. Let f be µ-strongly convex, and let x k+1 , y k+1 and λ k+1 be computed as per Alg. 2. For all x ∈ X and y ∈ Y, and w ∈ Ω, it holds for k ≥ 0 that f (x k) − f (x) + h(y k+1) − h(y) + ⟨w k+1 − w, F (w k+1)⟩ ≤ η k 2 ∥g k ∥ 2 2 − µ 2 ∆ k + 1 2η k [∆ k − ∆ k+1 ] + β 2 [A k − A k+1 ] + 1 2β [L k − L k+1 ] + ⟨δ k , x k − x⟩. By the strong con...

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that only one of the two functions has...