  We address a decentralized convex optimization problem, where every agent has
its unique local objective function and constraint set. Agents compute at
different speeds, and their communication may be delayed and directed. For this
setup, we propose an asynchronous double averaging and gradient projection
(ASY-DAGP) algorithm. Our algorithm handles difficult scenarios such as message
failure, by employing local buffers and utilizing the temporal correlation in
the transmitted messages. We guarantee the convergence speed of our algorithm
using performance estimation problems (PEP). In particular, we introduce the
concept of the linear quadratic (LQ) PEP. This approach simplifies the analysis
of smooth convex optimization problems, going beyond Lyapunov function analyses
and avoiding restrictive assumptions such as strong-convexity. Numerical
experiments validate the effectiveness of our proposed algorithm.
