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We address a decentralized convex optimization problem, where every agent hasits unique local objective function and constraint set. Agents compute atdifferent speeds, and their communication may be delayed and directed. For thissetup, we propose an asynchronous double averaging and gradient projection(ASY-DAGP) algorithm. Our algorithm handles difficult scenarios such as messagefailure, by employing local buffers and utilizing the temporal correlation inthe transmitted messages. We guarantee the convergence speed of our algorithmusing performance estimation problems (PEP). In particular, we introduce theconcept of the linear quadratic (LQ) PEP. This approach simplifies the analysisof smooth convex optimization problems, going beyond Lyapunov function analysesand avoiding restrictive assumptions such as strong-convexity. Numericalexperiments validate the effectiveness of our proposed algorithm.

Asynchronous Decentralized Optimization with Constraints: Achievable Speeds of Convergence for Directed Graphs