Distributed Optimization With Local Domains: Applications in MPC and Network Flows

Abstract

In this paper we consider a network with $P$ nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector $x^{\star }$ minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function depends only on some components of the variable. Consequently, each node is interested in knowing only some components of $x^{\star }$, not the entire vector. This allows for improvement in communication-efficiency. We apply our algorithm to model predictive control (MPC) and to network flow problems and show, through experiments on large networks, that our proposed algorithm requires less communications to converge than prior algorithms.

Submitted to IEEE Trans. Aut. Control

References in corpus (2)

• On the Linear Convergence of the Alternating Direction Method of Multipliers
• Communication-Efficient Algorithms For Distributed Optimization

Cited by in corpus (17)

• Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning
• Diffusion LMS for Multitask Problems with Local Linear Equality Constraints
• Adaptation and learning over networks under subspace constraints -- Part I: Stability Analysis
• Quantization for decentralized learning under subspace constraints
• Distributed Gradient Methods with Variable Number of Working Nodes
• $\mathcal{C}\mathcal{I}\mathcal{R}\mathcal{FE}$: A Distributed Random Fields Estimator
• Generalized gradient optimization over lossy networks for partition-based estimation
• Extended ADMM and BCD for Nonseparable Convex Minimization Models with Quadratic Coupling Terms: Convergence Analysis and Insights
• Fast and Stable Nonconvex Constrained Distributed Optimization: The ELLADA Algorithm
• Communication-Efficient Algorithms For Distributed Optimization
• SI-ADMM: A Stochastic Inexact ADMM Framework for Stochastic Convex Programs
• A Partition-Based Implementation of the Relaxed ADMM for Distributed Convex Optimization over Lossy Networks
• A Fully Parallel Primal-Dual Algorithm for Centralized and Distributed Optimization
• In-Network Linear Regression with Arbitrarily Split Data Matrices
• Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition
• Cycle flow formulation of optimal network flow problems for centralized and decentralized solvers
• A randomized primal distributed algorithm for partitioned and big-data non-convex optimization