2 research outputs found
Distributed Continuous-Time and Discrete-Time Optimization With Nonuniform Unbounded Convex Constraint Sets and Nonuniform Stepsizes
This paper is devoted to distributed continuous-time and discrete-time
optimization problems with nonuniform convex constraint sets and nonuniform
stepsizes for general differentiable convex objective functions. The
communication graphs are not required to be strongly connected at any time, the
gradients of the local objective functions are not required to be bounded when
their independent variables tend to infinity, and the constraint sets are not
required to be bounded. For continuous-time multi-agent systems, a distributed
continuous algorithm is first introduced where the stepsizes and the convex
constraint sets are both nonuniform. It is shown that all agents reach a
consensus while minimizing the team objective function even when the constraint
sets are unbounded. After that, the obtained results are extended to
discrete-time multi-agent systems and then the case where each agent remains in
a corresponding convex constraint set is studied. To ensure all agents to
remain in a bounded region, a switching mechanism is introduced in the
algorithms. It is shown that the distributed optimization problems can be
solved, even though the discretization of the algorithms might deviate the
convergence of the agents from the minimum of the objective functions. Finally,
numerical examples are included to show the obtained theoretical results.Comment: 11 pages, 3figure
Distributed Mirror Descent with Integral Feedback: Asymptotic Convergence Analysis of Continuous-time Dynamics
This work addresses distributed optimization, where a network of agents wants
to minimize a global strongly convex objective function. The global function
can be written as a sum of local convex functions, each of which is associated
with an agent. We propose a continuous-time distributed mirror descent
algorithm that uses purely local information to converge to the global optimum.
Unlike previous work on distributed mirror descent, we incorporate an integral
feedback in the update, allowing the algorithm to converge with a constant
step-size when discretized. We establish the asymptotic convergence of the
algorithm using Lyapunov stability analysis. We further illustrate numerical
experiments that verify the advantage of adopting integral feedback for
improving the convergence rate of distributed mirror descent