1,087 research outputs found
Improved Convergence Rates for Distributed Resource Allocation
In this paper, we develop a class of decentralized algorithms for solving a
convex resource allocation problem in a network of agents, where the agent
objectives are decoupled while the resource constraints are coupled. The agents
communicate over a connected undirected graph, and they want to collaboratively
determine a solution to the overall network problem, while each agent only
communicates with its neighbors. We first study the connection between the
decentralized resource allocation problem and the decentralized consensus
optimization problem. Then, using a class of algorithms for solving consensus
optimization problems, we propose a novel class of decentralized schemes for
solving resource allocation problems in a distributed manner. Specifically, we
first propose an algorithm for solving the resource allocation problem with an
convergence rate guarantee when the agents' objective functions are
generally convex (could be nondifferentiable) and per agent local convex
constraints are allowed; We then propose a gradient-based algorithm for solving
the resource allocation problem when per agent local constraints are absent and
show that such scheme can achieve geometric rate when the objective functions
are strongly convex and have Lipschitz continuous gradients. We have also
provided scalability/network dependency analysis. Based on these two
algorithms, we have further proposed a gradient projection-based algorithm
which can handle smooth objective and simple constraints more efficiently.
Numerical experiments demonstrates the viability and performance of all the
proposed algorithms
A geometrically converging dual method for distributed optimization over time-varying graphs
In this paper we consider a distributed convex optimization problem over
time-varying undirected networks. We propose a dual method, primarily averaged
network dual ascent (PANDA), that is proven to converge R-linearly to the
optimal point given that the agents objective functions are strongly convex and
have Lipschitz continuous gradients. Like dual decomposition, PANDA requires
half the amount of variable exchanges per iterate of methods based on DIGing,
and can provide with practical improved performance as empirically
demonstrated.Comment: Submitted to Transactions on Automatic Contro
- …