Related papers: Efficient Consensus Model based on Proximal Gradie…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
Recently convolutional sparse representation (CSR), as a sparse representation technique, has attracted increasing attention in the field of image processing, due to its good characteristic of translate-invariance. The content of CSR…
We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…
We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…
In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the…
This paper introduces the Bi-linear consensus Alternating Direction Method of Multipliers (Bi-cADMM), aimed at solving large-scale regularized Sparse Machine Learning (SML) problems defined over a network of computational nodes.…
The parallel alternating direction method of multipliers (ADMM) algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large…
We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent…
Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the…
This paper proposes a fast decentralized algorithm for solving a consensus optimization problem defined in a directed networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form, and are…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
ADMM is a popular algorithm for solving convex optimization problems. Applying this algorithm to distributed consensus optimization problem results in a fully distributed iterative solution which relies on processing at the nodes and…
Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…