  This paper studies the application of the blended dynamics approach towards
distributed optimization problem where the global cost function is given by a
sum of local cost functions. The benefits include (i) individual cost function
need not be convex as long as the global cost function is strongly convex and
(ii) the convergence rate of the distributed algorithm is arbitrarily close to
the convergence rate of the centralized one. Two particular continuous-time
algorithms are presented using the proportional-integral-type couplings. One
has benefit of `initialization-free,' so that agents can join or leave the
network during the operation. The other one has the minimal amount of
communication information. After presenting a general theorem that can be used
for designing distributed algorithms, we particularly present a distributed
heavy-ball method and discuss its strength over other methods.
