This paper introduces a modified version of the alternating direction method of multipliers (ADMM) for distributed optimization. While the current ADMM algorithms have shown promising results in finding near-optimal solutions for various convex and non-convex optimization problems, it is still uncertain whether they can converge to a stationary point for weakly convex and locally non-smooth functions. By utilizing the Moreau envelope function, our analysis demonstrates that our proposed method, called MADM, can indeed converge to a stationary point under mild conditions. We also calculate the bounds on the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Additionally, our numerical experiments indicate that MADM is faster and more robust compared to commonly used approaches.
Decentralized Weakly Convex Optimization with Moreau Envelope ADMM
