This note considers multi-agent systems seeking to optimize a convex ag-gregate function. We assume that the gradient of this function is distributed, mean-ing that each agent can compute its corresponding partial derivative with informa-tion about its neighbors and itself only. In such scenarios, the discrete-time imple-mentation of the gradient descent method poses the basic challenge of determining
appropriate agent stepsizes that guarantee the monotonic evolution of the objective
function. We provide a distributed algorithmic solution to this problem based on
the aggregation of agent stepsizes via adaptive convex combinations. Simulations
illustrate our results.
