  We propose a distributed solution for a constrained convex optimization
problem over a network of clustered agents each consisted of a set of
subagents. The communication range of the clustered agents is such that they
can form a connected undirected graph topology. The total cost in this
optimization problem is the sum of the local convex costs of the subagents of
each cluster. We seek a minimizer of this cost subject to a set of affine
equality constraints, and a set of affine inequality constraints specifying the
bounds on the decision variables if such bounds exist. We design our
distributed algorithm in a cluster-based framework which results in a
significant reduction in communication and computation costs. Our proposed
distributed solution is a novel continuous-time algorithm that is linked to the
augmented Lagrangian approach. It converges asymptotically when the local cost
functions are convex and exponentially when they are strongly convex and have
Lipschitz gradients. Moreover, we use an $\epsilon$-exact penalty function to
address the inequality constraints and derive an explicit lower bound on the
penalty function weight to guarantee convergence to $\epsilon$-neighborhood of
the global minimum value of the cost. A numerical example demonstrates our
results.
