Distributed Time-Varying Quadratic Optimization for Multiple Agents Under Undirected Graphs

This paper considers a class of distributed quadratic optimization problem under an undirected and connected graph. Different from most of the existing distributed optimization works that consider the optimal solutions to be constants, the optimal solution and the objective functions at the optimal solution are both assumed to be time varying. For the case where there is no constraint on the decision variables, gradient-based searching methods are proposed to track the unknown optimal solution. The tracking errors are proven to be asymptotically stable. For the case where there exists a local compact convex constraint set for each agent, projected gradient-based methods are proposed for both neighboring coupled and generally coupled objective functions, and the tracking errors are proven to be uniformly ultimately bounded with arbitrarily small bound.