Proportional integral distributed optimization for dynamic network topologies

Abstract

This paper investigates proportional-integral distributed optimization when the underlying information exchange network is dynamic. Proportional-integral distributed optimization is a technique which combines consensus-based methods and dual-decomposition methods to form a method which has the convergence guarantees of dual-decomposition and the damped response of the consensus methods. This paper extends PI distributed optimization to allow for dynamic communication networks, permitting agents to change who they can communicate with, without sacrificing convergence to the collective optimum.

Cloud-based optimization: A quasi-decentralized approach to multi-agent coordination

“…The cloud computer is taken to be capable of large batch computations and receives periodic transmissions from each agent containing each agent's own state. The cloud computer uses the agents' states to compute the next value of µ using Equation (6) and then transmits the states it received and the newly computed µ vector to each agent. Each agent then uses the information from the cloud to update its own state in the vein of (7).…”

“…At timestep 0, each agent takes one gradient step to update its own state according to Equation (7). Simultaneously, and also at timestep 0, the cloud takes one gradient step to update the KT multipliers in the cloud according to Equation (6). Then at timestep 1, agent i sends its state, x i i (1), to the cloud.…”

“…Distributed optimization and algorithms have received significant attention during the last decade, e.g., [1], [20], [10], [8], [15], [22], [6], due to the emergence of a number of application domains in which individual decision makers have to collectively arrive at a decision in a distributed manner. Examples of these applications include communication networks [12], [5], sensor networks [13], [23], [2], multirobot systems [26], [21], and smart power grids [3].…”

Passivity-Based Distributed Optimization With Communication Delays Using PI Consensus Algorithm

“…All of the above papers address so-called resource allocation problems [17] or its variations. In this paper, we deal with another type of distributed optimization studied in [18]- [27]. Nedić and Ozdaglar [18] present a distributed algorithm which combines consensus algorithms and subgradient methods.…”

“…Fair comparison with these articles is difficult due to considerably different problem settings, but in general they do not prove exact convergence to the optimal solution whereas we do. The secondary contribution is to reveal that the problem in [18]- [27] can be treated within the passivity paradigm. Thirdly, we handle general convex inequality constraints in this paper, while the other passivity-based approaches [10]- [16] take only linear and/or scalar constraints.…”