  We consider a general multi-agent convex optimization problem where the
agents are to collectively minimize a global objective function subject to a
global inequality constraint, a global equality constraint, and a global
constraint set. The objective function is defined by a sum of local objective
functions, while the global constraint set is produced by the intersection of
local constraint sets. In particular, we study two cases: one where the
equality constraint is absent, and the other where the local constraint sets
are identical. We devise two distributed primal-dual subgradient algorithms
which are based on the characterization of the primal-dual optimal solutions as
the saddle points of the Lagrangian and penalty functions. These algorithms can
be implemented over networks with changing topologies but satisfying a standard
connectivity property, and allow the agents to asymptotically agree on optimal
solutions and optimal values of the optimization problem under the Slater's
condition.
