Distributed line search via dynamic convex combinations

This paper considers multi-agent systems seeking to optimize a convex aggregate function. We assume that the gradient of this function is distributed, meaning that each agent can compute its corresponding partial derivative with state information about its neighbors and itself only. In such scenarios, the discrete-time implementation of the gradient descent method poses the fundamental 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.