Accelerated Dual Averaging Methods for Decentralized Constrained Optimization

In this article, we study decentralized convex constrained optimization problems in networks. We focus on the dual averaging-based algorithmic framework that is well-documented to be superior handling constraints and complex communication environments simultaneously. Two new averaging (DDA) algorithms are proposed. first one, a second-order dynamic average consensus protocol tailored for DDA-type algorithms, which equips each agent with provably more accurate estimate of global variable than conventional schemes. rigorously prove proposed algorithm attains $\mathcal {O}(1/t)$ convergence general smooth problems, existing DDA methods were only known converge at {O}(1/\sqrt{t})$ prior our work. second use extrapolation technique accelerate DDA. Compared accelerated where typically two different variables exchanged among agents time, seeks local gradients. Then, performed based sequences primal variables, determined by accumulations gradients consecutive time instants, respectively. The proved {O}(1)\left(\frac{1}{t^{2}}+\frac{1}{t(1-\beta)^{2}}\right)$ , notation="LaTeX">$\beta$ denotes largest singular value mixing matrix. remark condition parameter guarantee does not rely spectrum matrix, making itself easy satisfy practice. Finally, numerical results presented demonstrate efficiency methods.