In this paper, we propose the Bregman Douglas-Rachford splitting (BDRS) method and its variant Bregman Peaceman-Rachford splitting method for solving maximal monotone inclusion problem. We show that BDRS is equivalent to a Bregman alternating direction method of multipliers (ADMM) when applied to the dual of the problem. A special case of the Bregman ADMM is … Read more
We consider the Lasserre hierarchy for computing bounds on the stability number of graphs. The semidefinite programs (SDPs) arising from this hierarchy involve large matrix variables and many linear constraints, which makes them difficult to solve using interior-point methods. We propose solving these SDPs using the alternating direction method of multipliers (ADMM). When the second … Read more
We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents’ preferences fairly, we focus on finding a core solution. For divisible items, a core solution always exists and can be calculated by maximizing the Nash welfare objective. However, such a … Read more
Block-structured quadratic programs (QPs) frequently arise in the context of the direct approach to solving optimal control problems. For successful application of direct optimal control algorithms to many real-world problems it is paramount that these QPs can be solved efficiently and reliably. Besides interior-point methods and active-set methods, ADMM-based quadratic programming approaches have gained popularity. … Read more
In this paper, we focus on a linearly constrained composite minimization problem whose objective function is possibly nonsmooth and nonconvex. Unlike the traditional construction of augmented Lagrangian function, we provide a proximal-perturbed augmented Lagrangian and then develop a new Bregman Alternating Direction Method of Multipliers (ADMM). Under mild assumptions, we show that the novel augmented … Read more
Decomposition using consensus ADMM can be used to allow parallelization efficiencies or for reasons related to information security. In either case,the input data may be uncertain and we give a decomposition algorithm. ArticleDownload View PDF
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important generalization of the Matrix Completion problem, a central problem in Statistics, Operations Research and Machine Learning, that arises … Read more
Recently, semidefinite programming performance estimation has been employed as a strong tool for the worst-case performance analysis of first order methods. In this paper, we derive new non-ergodic convergence rates for the alternating direction method of multipliers (ADMM) by using performance estimation. We give some examples which show the exactness of the given bounds. We … Read more
This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze the stationary solution of the proposed formulation, obtaining a sufficient condition … Read more
In this paper, an inexact Alternating Direction Method of Multipliers (ADMM) has been proposed for solving the two-block separable convex optimization problem subject to linear equality constraints. The first resulting subproblem is solved inexactly under relative error criterion, while another subproblem called regularization problem is solved inexactly by introducing an indefinite proximal term. Meanwhile, the … Read more