  In this work, we establish convergence results for the distributed proximal
point algorithm (DPPA) for distributed optimization problems. We consider the
problem on the whole domain Rd and find a general condition on the stepsize and
cost functions such that the DPPA is stable. We prove that the DPPA with
stepsize $\eta > 0$ exponentially converges to an $O(\eta)$-neighborhood of the
optimizer. Our result clearly explains the advantage of the DPPA with respect
to the convergence and stability in comparison with the distributed gradient
descent algorithm. We also provide numerical tests supporting the theoretical
results.
