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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…
Non-convex constrained optimizations are ubiquitous in robotic applications such as multi-agent navigation, UAV trajectory optimization, and soft robot simulation. For this problem class, conventional optimizers suffer from small step sizes…
For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
In this paper, we consider solving multiple-block separable convex minimization problems using alternating direction method of multipliers (ADMM). Motivated by the fact that the existing convergence theory for ADMM is mostly limited to the…
As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…
In this paper we consider minimization of a difference-of-convex (DC) function with and without linear constraints. We first study a smooth approximation of a generic DC function, termed difference-of-Moreau-envelopes (DME) smoothing, where…
The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying…
Recently, the alternating direction method of multipliers (ADMM) has found many efficient applications in various areas; and it has been shown that the convergence is not guaranteed when it is directly extended to the multiple-block case of…
Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
Convergence rates are established for an inexact accelerated alternating direction method of multipliers (I-ADMM) for general separable convex optimization with a linear constraint. Both ergodic and non-ergodic iterates are analyzed.…
The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various convex or nonconvex composite problems that arise in the fields of image & signal processing and machine…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian…