  In this paper, the distributed resource allocation optimization problem is
investigated. The allocation decisions are made to minimize the sum of all the
agents' local objective functions while satisfying both the global network
resource constraint and the local allocation feasibility constraints. Here the
data corresponding to each agent in this separable optimization problem, such
as the network resources, the local allocation feasibility constraint, and the
local objective function, is only accessible to individual agent and cannot be
shared with others, which renders new challenges in this distributed
optimization problem. Based on either projection or differentiated projection,
two classes of continuous-time algorithms are proposed to solve this
distributed optimization problem in an initialization-free and scalable manner.
Thus, no re-initialization is required even if the operation environment or
network configuration is changed, making it possible to achieve a
"plug-and-play" optimal operation of networked heterogeneous agents. The
algorithm convergence is guaranteed for strictly convex objective functions,
and the exponential convergence is proved for strongly convex functions without
local constraints. Then the proposed algorithm is applied to the distributed
economic dispatch problem in power grids, to demonstrate how it can achieve the
global optimum in a scalable way, even when the generation cost, or system
load, or network configuration, is changing.
