  This work investigates the distributed constrained optimization problem under
inter-agent communication delays from the perspective of passivity. First, we
propose a continuous-time algorithm for distributed constrained optimization
with general convex objective functions. The asymptotic stability under general
convexity is guaranteed by the phase lead compensation. The inequality
constraints are handled by adopting a projection-free generalized Lagrangian,
whose primal-dual gradient dynamics preserves passivity and smoothness,
enabling the application of the LaSalle's invariance principle in the presence
of delays. Then, we incorporate the scattering transformation into the proposed
algorithm to enhance the robustness against unknown and heterogeneous
communication delays. Finally, a numerical example of a matching problem is
provided to illustrate the results.
