This paper develops a unified distributed method for solving two classes of
constrained networked optimization problems, i.e., optimal consensus problem
and resource allocation problem with non-identical set constraints. We first
transform these two constrained networked optimization problems into a unified
saddle-point problem framework with set constraints. Subsequently, two
projection-based primal-dual algorithms via Optimistic Gradient Descent Ascent
(OGDA) method and Extra-gradient (EG) method are developed for solving
constrained saddle-point problems. It is shown that the developed algorithms
achieve exact convergence to a saddle point with an ergodic convergence rate
O(1/k) for general convex-concave functions. Based on the proposed
primal-dual algorithms via saddle-point dynamics, we develop unified
distributed algorithm design and convergence analysis for these two networked
optimization problems. Finally, two numerical examples are presented to
demonstrate the theoretical results