distributed optimization

An Augmented Lagrangian based Algorithm for Distributed Non-Convex Optimization

  • Moritz Diehl
  • Janick V Frasch
  • Boris Houska
    • Categories Constrained Nonlinear Optimization Tags , ,

    This paper is about distributed derivative-based algorithms for solving optimization problems with a separable (potentially nonconvex) objective function and coupled affine constraints. A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms. The method negotiates shared dual variables that may be interpreted as prices, a concept … Read more

    Distributed Optimization Methods for Large Scale Optimal Control

  • Attila Kozma
    • Categories Optimization of Simulated Systems, Quadratic Programming Tags , , , , ,

    This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. … Read more

    On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers

  • Wei Deng
  • Wotao Yin
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , ,

    The formulation min f(x)+g(y) subject to Ax+By=b, where f and g are extended-value convex functions, arises in many application areas such as signal processing, imaging and image processing, statistics, and machine learning either naturally or after variable splitting. In many common problems, one of the two objective functions is strictly convex and has Lipschitz continuous … Read more

    Distributed Basis Pursuit

  • Pedro Aguiar
  • João Mota
  • Markus Püschel
  • João Xavier
    • Categories Convex Optimization, Network Optimization, Parallel Algorithms Tags , , ,

    We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize … Read more

    Dynamic Network Utility Maximization with Delivery Contracts

  • Stephen Boyd
  • Nikolaos Trichakis
  • Argyrios Zymnis
    • Categories Network Optimization Tags , ,

    We consider a multi-period variation of the network utility maximization problem that includes delivery constraints. We allow the flow utilities, link capacities and routing matrices to vary over time, and we introduce the concept of delivery contracts, which couple the flow rates across time. We describe a distributed algorithm, based on dual decomposition, that solves … Read more