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The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a…
It is widely acknowledged that hyperparameter selection plays a critical role in the effectiveness of sparse optimization problems. The bilevel optimization provides a robust framework for addressing this issue, but these existing methods…
The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates…
The matrix low-rank approximation problem with additional convex constraints can find many applications and has been extensively studied before. However, this problem is shown to be nonconvex and NP-hard; most of the existing solutions are…
In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and…
Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…
We propose a distributed optimization method for solving a distributed model predictive consensus problem. The goal is to design a distributed controller for a network of dynamical systems to optimize a coupled objective function while…
This paper discusses a consensus-based alternating direction method of multipliers (ADMM) approach to solve the multi-area coordinated network-constrained unit commitment (NCUC) problem in a distributed manner. Due to political and…
In this paper, we analyze the convergence of Alternating Direction Method of Multipliers (ADMM) on convex quadratic programs (QPs) with linear equality and bound constraints. The ADMM formulation alternates between an equality constrained…
This paper studies a proximal alternating direction method of multipliers (ADMM) with variable metric indefinite proximal terms for linearly constrained convex optimization problems. The proximal ADMM plays an important role in many…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
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…
Alternating Direction Method of Multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting agents locally estimate the optimal solution of an…
From a dual perspective of the sparse representation model, Nam et al. proposed the cosparse analysis model. In this paper, we aim to investigate the convergence of the alternating direction method of multipliers (ADMM) for the cosparse…
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
We give a general proof of convergence for the Alternating Direction Method of Multipliers (ADMM). ADMM is an optimization algorithm that has recently become very popular due to its capabilities to solve large-scale and/or distributed…
Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers…
In this paper, we discuss a family of robust, high-dimensional regression models for quantile and composite quantile regression, both with and without an adaptive lasso penalty for variable selection. We reformulate these quantile…
We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available…
Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require…