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. Article Download View Consensus ADMM Under Uncertainty
\(\) 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 … 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
Decarbonization via the integration of renewables poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take advantage of these opportunities while providing flexibility to power systems that can help address these challenges. We propose a solution method for the optimal control of multiple price-maker electric energy storage … Read more
This short paper describes a simple subgradient-based techniques for deriving bounds on the optimal solution value when using the ADMM to solve convex optimization problems. The technique requires a bound on the magnitude of some optimal solution vector, but is otherwise completely general. Some computational examples using LASSO problems demonstrate that the technique can produce … Read more
This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact version of the proximal point algorithm that includes both an inertial step and overrelaxation. We apply our new inexact ADMM method … Read more
We consider spot-market trading of electricity including storage operators as additional agents besides producers and consumers. Storages allow for shifting produced electricity from one time period to a later one. Due to this, multiple market equilibria may occur even if classical uniqueness assumptions for the case without storages are satisfied. For models containing storage operators, … Read more
In this paper, we propose a new framework to implement interior point method (IPM) in order to solve some very large scale linear programs (LP). Traditional IPMs typically use Newton’s method to approximately solve a subproblem that aims to minimize a log-barrier penalty function at each iteration. Due its connection to Newton’s method, IPM is … Read more