相关论文: On the Duality Gap Convergence of ADMM Methods

Due to the explosion in size and complexity of modern data sets and privacy concerns of data holders, it is increasingly important to be able to solve machine learning problems in distributed manners. The Alternating Direction Method of…

In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that…

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 the past decades, intensive efforts have been put to design various loss functions and metric forms for metric learning problem. These improvements have shown promising results when the test data is similar to the training data. However,…

The Alternating Direction Method of Multipliers (ADMM) has now days gained tremendous attentions for solving large-scale machine learning and signal processing problems due to the relative simplicity. However, the two-block structure of the…

When solving consensus optimization problems over a graph, there is often an explicit characterization of the convergence rate of Gradient Descent (GD) using the spectrum of the graph Laplacian. The same type of problems under the…

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…

The parallel alternating direction method of multipliers (ADMM) algorithms have gained popularity in statistics and machine learning due to their efficient handling of large sample data problems. However, the parallel structure of these…

The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of…

Distributed optimization is fundamental to large-scale machine learning and control applications. Among existing methods, the alternating direction method of multipliers (ADMM) has gained popularity due to its strong convergence guarantees…

In this paper, we consider a proximal linearized alternating direction method of multipliers (PL-ADMM) for solving linearly constrained nonconvex and possibly nonsmooth optimization problems. The algorithm is generalized by using variable…

Pipeline parallelism is essential for large-scale model training, but existing asynchronous approaches often degrade convergence due to parameter mismatch between forward and backward passes. We propose Asynchronous Multi-Directional…

The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…

In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for…

Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…

Dual ascent (DA) and the method of multipliers (MM) are fundamental methods for solving linear equality-constrained convex optimization problems, and their dual updates can be viewed as the minimization of a proximal linear surrogate…

The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance. The convergence properties of the 2-block ADMM have been…

We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…

In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm…