Browsing by Author "Ling, Q."
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Item A Linearized Bregman Algorithm for Decentralized Basis Pursuit(2013-04) Yuan, K.; Ling, Q.; Yin, W.; Ribeiro, A.We solve a decentralized basis pursuit problem in a multiagent system, where each agent holds part of the linear observations on a common sparse vector, and all the agents collaborate to recover the sparse vector through limited neighbor-to-neighbor communication. The proposed decentralized linearized Bregman algorithm solves the Lagrange dual of an augmented l1 model that is equivalent to basis pursuit. The fact that this dual problem is unconstrained and differentiable enables a lightweight yet efficient decentralized gradient algorithm. We prove nearly linear convergence of the algorithm in the sense that uniformly for every agent i, the error obeys |x_i(k) - x*|<=e(k) and e(k)<=rho e(k-1)+gamma, where rho<=1 and gamma>=0 are independent of k or i. Numerical experiments demonstrate this convergence.Item Linearly Convergent Decentralized Consensus Optimization with the Alternating Direction Method of Multipliers(2013-04) Shi, W.; Ling, Q.; Yuan, K.; Wu, G.; Yin, W.In a decentralized consensus optimization problem, a network of agents minimizes the summation of their local objective functions on a common set of decision variables, allowing only information exchange among neighbors. The alternating direction method of multipliers (ADMM) has been shown to be a powerful tool for solving the problem with empirically fast convergence. This paper establishes the linear convergence rate of the ADMM in decentralized consensus optimization. The theoretical convergence rate is a function of the network topology, properties of the local objective functions, and the algorithm parameter. This result not only gives a performance guarantee for the ADMM but also provides a guideline to accelerate its convergence for decentralized consensus optimization problems.