  A novel distributed algorithm is proposed for finite-time converging to a
feasible consensus solution satisfying global optimality to a certain accuracy
of the distributed robust convex optimization problem (DRCO) subject to bounded
uncertainty under a uniformly strongly connected network. Firstly, a
distributed lower bounding procedure is developed, which is based on an outer
iterative approximation of the DRCO through the discretization of the compact
uncertainty set into a finite number of points. Secondly, a distributed upper
bounding procedure is proposed, which is based on iteratively approximating the
DRCO by restricting the constraints right-hand side with a proper positive
parameter and enforcing the compact uncertainty set at finitely many points.
The lower and upper bounds of the global optimal objective for the DRCO are
obtained from these two procedures. Thirdly, two distributed termination
methods are proposed to make all agents stop updating simultaneously by
exploring whether the gap between the upper and the lower bounds reaches a
certain accuracy. Fourthly, it is proved that all the agents finite-time
converge to a feasible consensus solution that satisfies global optimality
within a certain accuracy. Finally, a numerical case study is included to
illustrate the effectiveness of the distributed algorithm.
