ABSTRACT
The alternating direction method of multiplier (ADMM) is a distributed convex optimization algorithm that solves a wide range of convex optimization problems. This chapter reviews the ADMM algorithm together with some of its variants. It shows that many network applications can be expressed as optimization problems on connected graphs and solved effectively and efficiently by the ADMM. The chapter explores different ways of parallelizing the ADMM for the distributed model fitting problems and presents the consensus ADMM for distributed network analyses. In network applications, data are often collected and stored across a distributed network consisting of computing nodes from different locations. For many of these applications, the problems to be solved can be reduced to distributed model fitting across a connected network. The network lasso problem is a convex optimization problem and can be efficiently solved for small networks via generic convex optimization algorithms.
