A Communication-Efficient Distributed Optimization Algorithm with Coupled Constraints

This paper designs a communication-efficient distributed optimization algorithm for optimization problems subject to coupled equality constraints. By means of duality theory, the original problem is reformulated to tackle the coupled equality constraints. Furthermore, compressed communication is employed to enhance efficiency whereas introducing compression errors that degrade the performance. To address this, differential compression techniques with dynamic scaling factors are incorporated into the algorithm design. It is shown that the proposed distributed compressed algorithm achieves linear convergence under different compressors. Numerical results further demonstrate its robust performance under different types of compressors while satisfying the equality constraints.

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