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This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM) for solving convex problem: minimize f1(x1) + • • • + fN (xN) subject to A1x1 + • • • + AN xN = c, The algorithm decomposes the original problem into N smaller subproblems and solves them in parallel at each iteration. This Jacobian-type(More)
—This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under certain gRIP condition in the noise free case. While in the noisy(More)
Finding a fixed point to a nonexpansive operator, i.e., x * = T x * , abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update x in an asynchronous parallel fashion.(More)
This paper focuses on the coordinate update method, which is useful for solving large-sized problems involving linear and nonlinear mappings, and smooth and nonsmooth functions. It decomposes a problem into simple subproblems, where each subproblem updates one, or a small block of, variables. The coordinate update method sits at a high level of abstraction(More)
TMAC is a toolbox written in C++11 that implements algorithms based on a set of modern methods for large-scale optimization. It covers a variety of optimization problems, which can be both smooth and nonsmooth, convex and nonconvex, as well as constrained and unconstrained. The algorithms implemented in TMAC, such as the coordinate update method and(More)
Nickel compounds are environmental and occupational hazards that pose serious health problems and are causative factors of acute lung injury. The c-jun N-terminal kinases (JNKs) are regulated through a mitogen-activated protein (MAP) 3 kinase-MAP2 kinase cascade and have been implicated in nickel toxicity. In this study, we used genetically modified cells(More)
In recent studies on sparse modeling, l q (0 < q < 1) regularized least squares regression (l q LS) has received considerable attention due to its superiorities on sparsity-inducing and bias-reduction over the convex counterparts. In this paper, we propose a Gauss-Seidel iterative thresholding algorithm (called GAITA) for solution to this problem. Different(More)
Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we call delay, is the number of times it has(More)
The problem of finding a fixed point to a nonexpansive operator is an abstraction of many models in numerical linear algebra, optimization, and other areas of scientific computing. To solve this problem, we propose ARock, an asynchronous parallel algorithmic framework, in which a set of agents (machines, processors, or cores) update randomly selected(More)