admm

A proximal-perturbed Bregman ADMM for solving nonsmooth and nonconvex optimization problems

  • Jianchao Bai
    • Categories Nonsmooth Optimization Tags , , ,

    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

    Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM

  • Dimitris Bertsimas
  • Nicholas A. G. Johnson
    • Categories Data Science Algorithms, Nonlinear Optimization Tags , , ,

    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

    The exact worst-case convergence rate of the alternating direction method of multipliers

  • Moslem Zamani
  • Hadi Abbaszadehpeivasti
  • Etienne de Klerk
    • Categories Convex Optimization Tags , , ,

    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

    A Generalized Formulation for Group Selection via ADMM

  • Chengyu Ke
  • Sunyoung Shin
  • Yifei Lou
  • Miju Ahn
    • Categories Nonlinear Optimization Tags , , ,

    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

    An inexact ADMM with proximal-indefinite term and larger stepsize

  • Yuxue Ma
  • Jianchao Bai
    • Categories Convex Optimization Tags , , , ,

    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

    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