A Lie bracket approximation approach to distributed optimization over directed graphs
It provides a novel method for distributed optimization that relaxes typical connectivity requirements, benefiting multi-agent systems with directed communication.
The paper develops a distributed continuous-time optimization algorithm for problems with shared linear constraints over directed graphs, using Lie bracket approximation to achieve convergence under minimal assumptions on graph topology and constraint structure.
We consider a group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose topology is described by a time-invariant directed graph, by combining saddle-point dynamics with Lie bracket approximation techniques we derive a methodology that allows to design distributed continuous-time optimization algorithms that solve this problem under minimal assumptions on the graph topology as well as on the structure of the constraints. We discuss several extensions as well as special cases in which the proposed procedure becomes particularly simple.