admm

ADMM-based Unit and Time Decomposition for Price Arbitrage by Cooperative Price-Maker Electricity Storage Units

  • Miguel F. Anjos
  • James Cruise
  • Albert Solà Vilalta
    • Categories Convex Optimization, Dynamic Programming, Energy Tags , , , , , , ,

    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

    Deriving Solution Value Bounds from the ADMM

  • Jonathan Eckstein
    • Categories Convex Optimization, Nonsmooth Optimization Tags ,

    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

    Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms

  • M. Marques Alves
  • Jonathan Eckstein
  • Jefferson Gonçalves Melo
  • Marina Geremia
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    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

    On Electricity Market Equilibria with Storage: Modeling, Uniqueness, and a Distributed ADMM

  • Julia Grübel
  • Thomas Kleinert
  • Vanessa Krebs
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Galina Orlinskaya
    • Categories Convex Optimization, Parallel Algorithms, Quadratic Programming Tags , , , , , ,

    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

    An ADMM-Based Interior-Point Method for Large-Scale Linear Programming

  • Tianyi Lin
  • Shiqian Ma
  • Yinyu Ye
  • Shuzhong Zhang
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    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

    A Fully Distributed Dual Consensus ADMM Based on Partition for DC-OPF with Carbon Emission Trading

  • Zhaoyang Dong
  • Jiangyao Luo
  • Yan Xu
  • Linfeng Yang
  • Zhenrong Zhang
    • Categories Applications - Science and Engineering, Energy Tags , , , ,

    This paper presents a novel fully distributed alternating direction method of multipliers (ADMM) approach for solving the direct current optimal power flow with carbon emission trading (DC-OPF-CET) problem. Different from the other ADMM-based distributed approaches which disclosing boundary buses and branches information among adjacent subsystems, our proposed method adopts a new strategy by using ADMM … Read more

    Fast Multilevel Algorithms for Compressive Principle Component Pursuit

  • Vahan Hovhannisyan
  • Panos Parpas
  • Yannis Panagakis
  • Stefanos Zafeiriou
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , ,

    Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via principal component pursuit (PCP), recovers a low-rank matrix from sparse corruptions that are of unknown value and support by decomposing the observation matrix into two … Read more

    ADMM for Multiaffine Constrained Optimization

  • Frank E. Curtis
  • Wenbo Gao
  • Donald Goldfarb
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    We propose an expansion of the scope of the alternating direction method of multipliers (ADMM). Specifically, we show that ADMM, when employed to solve problems with multiaffine constraints that satisfy certain easily verifiable assumptions, converges to the set of constrained stationary points if the penalty parameter in the augmented Lagrangian is sufficiently large. When the … Read more

    Primal-Dual Optimization Algorithms over Riemannian Manifolds: an Iteration Complexity Analysis

  • Shiqian Ma
  • Junyu Zhang
  • Shuzhong Zhang
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing, image processing, and tensor PCA, among others. We develop an ADMM-like primal-dual approach based on decoupled solvable subroutines such as linearized proximal mappings. First, we introduce … Read more

    A Hierarchical Alternating Direction Method of Multipliers for Fully Distributed Unit Commitment

  • Zhang Chen
    • Categories Applications - Science and Engineering Tags , ,

    Abstract—This paper discusses a hierarchical alternating direction method of multipliers (ADMM) approach for the unit commitment (UC) problem in a fully distributed manner. Decentralized unit commitment operation schemes have several advantages when compared with the traditional centralized management system for smart grid. Specifically, decentralized management is more flexible, less computationally intensive, and easier to implement … Read more