  In this work, we propose a continuous-time distributed optimization algorithm
with guaranteed zero coupling constraint violation and apply it to safe
distributed control in the presence of multiple control barrier functions
(CBF). The optimization problem is defined over a network that collectively
minimizes a separable cost function with coupled linear constraints. An
equivalent optimization problem with auxiliary decision variables and a
decoupling structure is proposed. A sensitivity analysis demonstrates that the
subgradient information can be computed using local information. This then
leads to a subgradient algorithm for updating the auxiliary variables. A case
with sparse coupling constraints is further considered, and it is shown to have
better memory and communication efficiency. For the specific case of a
CBF-induced time-varying quadratic program (QP), an update law is proposed that
achieves finite-time convergence. Numerical results involving a static resource
allocation problem and a safe coordination problem for a multi-agent system
demonstrate the efficiency and effectiveness of our proposed algorithms.
