A System Theoretical Perspective to Gradient-Tracking Algorithms for Distributed Quadratic Optimization

11/15/2019
by   Michelangelo Bin, et al.
0

In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up. Specifically, we focus on a scenario in which agents in a static network want to cooperatively minimize the sum of quadratic cost functions. We show that the gradient tracking distributed algorithm for the investigated program can be viewed as a sparse closed-loop linear system in which the dynamic state-feedback controller includes consensus matrices and optimization (stepsize) parameters. The closed-loop system turns out to be not completely reachable and asymptotic stability can be shown restricted to a proper invariant set. Convergence to the global minimum, in turn, can be obtained only by means of a proper initialization. The proposed system interpretation of the distributed algorithm provides also additional insights on other structural properties and possible design choices that are discussed in the last part of the paper as a starting point for future developments.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/04/2022

Triggered Gradient Tracking for Asynchronous Distributed Optimization

This paper proposes Asynchronous Triggered Gradient Tracking, i.e., a di...
research
11/24/2020

Linear Convergence of Distributed Mirror Descent with Integral Feedback for Strongly Convex Problems

Distributed optimization often requires finding the minimum of a global ...
research
05/13/2023

Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus

This paper considers the problem of distributed multi-agent learning, wh...
research
02/10/2020

Convergence Guarantees of Policy Optimization Methods for Markovian Jump Linear Systems

Recently, policy optimization for control purposes has received renewed ...
research
03/31/2020

A Robust Gradient Tracking Method for Distributed Optimization over Directed Networks

In this paper, we consider the problem of distributed consensus optimiza...
research
02/11/2022

Distributed saddle point problems for strongly concave-convex functions

In this paper, we propose GT-GDA, a distributed optimization method to s...
research
01/20/2019

CASCLIK: CasADi-Based Closed-Loop Inverse Kinematics

A Python module for rapid prototyping of constraint-based closed-loop in...

Please sign up or login with your details

Forgot password? Click here to reset