A unitary distributed subgradient method for multiagent optimization with different coupling sources Abstract   Distributed optimization techniques offer high quality solutions to various engineering problems, such as resource allocation and distributed estimation and control. In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed subgradient method with double averaging (abbreviated as      DSA    2     ) that only requires peertopeer communication and local computation to solve the global problem. The algorithmic framework builds on dual methods and dynamic average consensus; the sequence of test points is formed by iteratively minimizing a local dual model of the overall objective where the coefficients, i.e., approximated subgradients of the objective, are supplied by the dynamic average consensus scheme. We theoretically show that      DSA    2      enjoys nonergodic convergence properties, i.e., the local minimizing sequence itself is convergent, a distinct feature that cannot be found in existing results. Specifically, we establish a convergence rate of     O   (    1      t      )      in terms of objective function error. Then, extensions are made to tackle distributed optimization problems with coupled functional constraints by combining      DSA    2      and dual decomposition. This is made possible by Lagrangian relaxation that transforms the coupling in constraints of the primal problem into that in cost functions of the dual, thus allowing us to solve the dual problem via      DSA    2     . Both the dual objective error and the quadratic penalty for the coupled constraint are proved to converge at a rate of     O   (    1      t      )     , and the primal objective error asymptotically vanishes. Numerical experiments and comparisons are conducted to illustrate the advantage of the proposed algorithms and validate our theoretical findings.

CommunicationCensored Linearized ADMM for Decentralized Consensus Optimization In this paper, we propose a communication and computationefficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node updates its local variable through combining neighboring variables and solving an optimization subproblem. The proposed algorithm, called as  co mmunicationcensored  l inearized  A DMM (COLA), leverages a linearization technique to reduce the iterationwise computation cost of ADMM and uses a communicationcensoring strategy to alleviate the communication cost. To be specific, COLA introduces successive linearization approximations to the local cost functions such that the resultant computation is firstorder and lightweight. Since the linearization technique slows down the convergence speed, COLA further adopts the communicationcensoring strategy to avoid transmissions of less informative messages. A node is allowed to transmit only if the distance between the current local variable and its previously transmitted one is larger than a censoring threshold. COLA is proven to be convergent when the local cost functions have Lipschitz continuous gradients and the censoring threshold is summable. When the local cost functions are further strongly convex, we establish the linear (sublinear) convergence rate of COLA, given that the censoring threshold linearly (sublinearly) decays to 0. Numerical experiments corroborate with the theoretical findings and demonstrate the satisfactory communicationcomputation tradeoff of COLA.